@article{cao_jing_liu_2024, title={A Spin Analog of the Plethystic Murnaghan-Nakayama Rule}, volume={2}, ISSN={["0219-3094"]}, url={https://doi.org/10.1007/s00026-023-00686-8}, DOI={10.1007/s00026-023-00686-8}, journal={ANNALS OF COMBINATORICS}, author={Cao, Yue and Jing, Naihuan and Liu, Ning}, year={2024}, month={Feb} }
 @article{jing_li_2024, title={A note on Cauchy's formula}, volume={153}, ISSN={["1090-2074"]}, url={https://doi.org/10.1016/j.aam.2023.102630}, DOI={10.1016/j.aam.2023.102630}, abstractNote={We use the correlation functions of vertex operators to give a proof of Cauchy's formula∏i=1K∏j=1N(1−xiyj)=∑μ⊆[K×N](−1)|μ|sμ{x}sμ′{y}. As an application of the interpretation, we obtain an expansion of ∏i=1∞(1−qi)i−1 in terms of half plane partitions.}, journal={ADVANCES IN APPLIED MATHEMATICS}, author={Jing, Naihuan and Li, Zhijun}, year={2024}, month={Feb} }
 @article{yang_jing_2024, title={Center of the Yangian double in type A}, volume={2}, ISSN={["1869-1862"]}, DOI={10.1007/s11425-022-2142-9}, journal={SCIENCE CHINA-MATHEMATICS}, author={Yang, Fan and Jing, Naihuan}, year={2024}, month={Feb} }
 @article{jing_liu_2024, title={Corrigendum to “The Green polynomials via vertex operators” [J. Pure Appl. Algebra 226 (2022) 107032]}, url={https://doi.org/10.1016/j.jpaa.2024.107670}, DOI={10.1016/j.jpaa.2024.107670}, journal={Journal of Pure and Applied Algebra}, author={Jing, Naihuan and Liu, Ning}, year={2024}, month={Sep} }
 @article{jing_li_wang_2024, title={Kostant's generating functions and Mckay-Slodowy correspondence}, volume={1}, ISSN={["1793-6829"]}, url={https://doi.org/10.1142/S0219498825501713}, DOI={10.1142/S0219498825501713}, abstractNote={Let [Formula: see text] be a pair of finite subgroups of [Formula: see text] and [Formula: see text] a finite-dimensional fundamental [Formula: see text]-module. We study Kostant’s generating functions for the decomposition of the [Formula: see text]-module [Formula: see text] restricted to [Formula: see text] in connection with the McKay–Slodowy correspondence. In particular, the classical Kostant formula was generalized to a uniform version of the Poincaré series for the symmetric invariants in which the multiplicities of any individual module in the symmetric algebra are completely determined.}, journal={JOURNAL OF ALGEBRA AND ITS APPLICATIONS}, author={Jing, Naihuan and Li, Zhijun and Wang, Danxia}, year={2024}, month={Jan} }
 @article{dobes_jing_2024, title={Qubits as hypermatrices and entanglement}, url={https://doi.org/10.1088/1402-4896/ad3989}, DOI={10.1088/1402-4896/ad3989}, abstractNote={Abstract In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $\pi$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle.}, journal={Physica Scripta}, author={Dobes, Isaac and Jing, Naihuan}, year={2024}, month={May} }
 @article{butorac_jing_kozic_yang_2024, title={Semi-infinite construction for the double Yangian of type A<sub>1</sub><SUP>(1)</SUP>}, volume={638}, ISSN={["1090-266X"]}, DOI={10.1016/j.jalgebra.2023.10.002}, abstractNote={We consider certain infinite dimensional modules of level 1 for the double Yangian DY(gl2) which are based on the Iohara–Kohno realization. We show that they possess topological bases of Feigin–Stoyanovsky-type, i.e. the bases expressed in terms of semi-infinite monomials of certain integrable operators which stabilize and satisfy the difference two condition. Finally, we give some applications of these bases to the representation theory of the corresponding quantum affine vertex algebra.}, journal={JOURNAL OF ALGEBRA}, author={Butorac, Marijana and Jing, Naihuan and Kozic, Slaven and Yang, Fan}, year={2024}, month={Jan}, pages={465–487} }
 @article{huang_jing_2024, title={Separability criteria based on the correlation tensor moments for arbitrary dimensional states}, volume={23}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-024-04262-8}, abstractNote={As one of the most profound features of quantum mechanics, entanglement is a vital resource for quantum information processing. Inspired by the recent work on PT-moments and separability [Phys. Rev. Lett. 127, 060504 (2021)], we propose two sets of separability criteria using moments of the correlation tensor for bipartite and multipartite quantum states, which are shown to be stronger in some aspects in detecting entanglement.}, number={2}, journal={QUANTUM INFORMATION PROCESSING}, author={Huang, Xiaofen and Jing, Naihuan}, year={2024}, month={Feb} }
 @article{cao_jing_wang_2024, title={Weighted monogamy and polygamy relations}, volume={21}, ISSN={["1612-202X"]}, DOI={10.1088/1612-202X/ad2921}, abstractNote={
 This research offers a comprehensive approach to strengthening both monogamous and polygamous relationships within the context of quantum correlations in multipartite quantum systems. We present the most stringent bounds for both monogamy and polygamy in multipartite systems compared to recently established relations. We show that whenever a bound is given (named it monogamy or polygamy), our bound indexed by some parameter s will always be stronger than the given bound. The study includes detailed examples, highlighting that our findings exhibit greater strength across all existing cases in comparison.}, number={4}, journal={LASER PHYSICS LETTERS}, author={Cao, Yue and Jing, Naihuan and Wang, Yiling}, year={2024}, month={Apr} }
 @article{zhao_hao_li_fei_jing_wang_2023, title={Detecting multipartite entanglement via complete orthogonal basis}, volume={54}, ISSN={["2211-3797"]}, DOI={10.1016/j.rinp.2023.107060}, abstractNote={We study genuine tripartite entanglement and multipartite entanglement in arbitrary n-partite quantum systems based on complete orthogonal basis (COB). While the usual Bloch representation of a density matrix uses three types of generators, the density matrix with COB operators has one uniformed type of generators which may simplify related computations. We take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement and multipartite entanglement. We first convert the general states to simpler forms by using the relationship between general symmetric informationally complete measurements and COB. Then we derive an operational criteria to detect genuine tripartite entanglement. We study multipartite entanglement in arbitrary dimensional multipartite systems. By providing detailed examples, we demonstrate that our criteria can detect more genuine entangled and multipartite entangled states than the previously existing criteria.}, journal={RESULTS IN PHYSICS}, author={Zhao, Hui and Hao, Jia and Li, Jing and Fei, Shao-Ming and Jing, Naihuan and Wang, Zhi-Xi}, year={2023}, month={Nov} }
 @article{hu_hu_yu_jing_2023, title={Enhanced quantum channel uncertainty relations by skew information}, volume={22}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-023-04113-y}, abstractNote={By revisiting the mathematical foundation of the uncertainty relation, skew information-based uncertainty sequences are developed for any two quantum channels. A reinforced version of the Cauchy-Schwarz inequality is adopted to improve the uncertainty relation, and a sampling technique of observables' coordinates is used to offset randomness in the inequality. It is shown that the lower bounds of the uncertainty relations are tighter than some previous studies.}, number={10}, journal={QUANTUM INFORMATION PROCESSING}, author={Hu, Xiaoli and Hu, Naihong and Yu, Bing and Jing, Naihuan}, year={2023}, month={Oct} }
 @article{zhang_jing_zhao_liu_ma_2023, title={Improved tests of genuine entanglement for multiqudits}, volume={143}, ISSN={["1286-4854"]}, url={https://doi.org/10.1209/0295-5075/acec0a}, DOI={10.1209/0295-5075/acec0a}, abstractNote={We give an improved criterion of genuine multipartite entanglement for an important class of multipartite quantum states using generalized Bloch representations of the density matrices. The practical criterion is designed based on the Weyl operators and can be used for detecting genuine multipartite entanglement in higher-dimensional systems. The test is shown to be significantly stronger than some of the most recent criteria.}, number={3}, journal={EPL}, author={Zhang, Xia and Jing, Naihuan and Zhao, Hui and Liu, Ming and Ma, Haitao}, year={2023}, month={Aug} }
 @article{jing_liu_2023, title={Murnaghan-Nakayama Rule and Spin Bitrace for the Hecke-Clifford Algebra}, volume={7}, ISSN={["1687-0247"]}, url={https://doi.org/10.1093/imrn/rnad158}, DOI={10.1093/imrn/rnad158}, abstractNote={
 A Pfaffian-type Murnaghan–Nakayama rule is derived for the Hecke–Clifford algebra $\mathcal{H}^{c}_{n}$ based on the Frobenius formula and vertex operators, and this leads to a combinatorial version via the tableaux realization of Schur’s $Q$-functions. As a consequence, a general formula for the irreducible characters $\zeta ^{\lambda }_{\mu }(q)$ using partition-valued functions is derived. Meanwhile, an iterative formula on the indexing partition $\lambda $ via the Pieri rule is also deduced. As applications, some compact formulae of the irreducible characters are given for special partitions and a symmetric property of the irreducible character is found. We also introduce the spin bitrace as the analogue of the bitrace for the Hecke algebra and derive its general combinatorial formula. Tables of irreducible characters are listed for $n\leq 7.$}, journal={INTERNATIONAL MATHEMATICS RESEARCH NOTICES}, author={Jing, Naihuan and Liu, Ning}, year={2023}, month={Jul} }
 @article{sun_jing_2023, title={O-operators and related structures on Leibniz algebras}, volume={1}, ISSN={["1532-4125"]}, DOI={10.1080/00927872.2022.2154783}, abstractNote={Abstract An -operator has been used to extend a Leibniz algebra by its representation. In this paper, we investigate several structures related to -operators on Leibniz algebras and introduce (dual) N-structures on Leibniz algebras associated to their representations. It is proved that -operators and dual N-structures generate each other under certain conditions. It is also shown that a solution of the strong Maurer-Cartan equation on the twilled Leibniz algebra gives rise to a dual N-structure. Finally, r – n structures, RBN-structures and -structures on Leibniz algebras are thoroughly studied and their interdependent relations are also studied.}, journal={COMMUNICATIONS IN ALGEBRA}, author={Sun, Qinxiu and Jing, Naihuan}, year={2023}, month={Jan} }
 @article{zhang_jing_liu_ma_2023, title={On monogamy and polygamy relations of multipartite systems}, volume={98}, ISSN={["1402-4896"]}, url={https://doi.org/10.1088/1402-4896/acbb37}, DOI={10.1088/1402-4896/acbb37}, abstractNote={We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the r-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.}, number={3}, journal={PHYSICA SCRIPTA}, author={Zhang, Xia and Jing, Naihuan and Liu, Ming and Ma, Haitao}, year={2023}, month={Mar} }
 @article{zhou_hu_jing_2023, title={On super quantum discord for high-dimensional bipartite state}, volume={22}, ISSN={["1573-1332"]}, url={https://doi.org/10.1007/s11128-023-04203-x}, DOI={10.1007/s11128-023-04203-x}, abstractNote={By quantifying the difference between quantum mutual information through weak measurement performed on a subsystem one is led to the notion of super quantum discord. The super version is also known to be difficult to compute as the quantum discord which was captured by the projective (strong) measurements. In this paper, we give effective bounds of the super quantum discord with or without phase damping channels for higher-dimensional bipartite quantum states, and found that the super version is always larger than the usual quantum discord as in the 2-dimensional case.}, number={12}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhou, Jianming and Hu, Xiaoli and Jing, Naihuan}, year={2023}, month={Dec} }
 @article{zhao_hao_fei_wang_jing_2023, title={One-particle loss detection of genuine multipartite entanglement}, volume={22}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-023-03916-3}, number={5}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhao, Hui and Hao, Jia and Fei, Shao-Ming and Wang, Zhi-Xi and Jing, Naihuan}, year={2023}, month={May} }
 @article{jiang_jing_liu_2023, title={Q-Kostka polynomials and spin Green polynomials}, volume={3}, ISSN={["1436-5081"]}, url={https://doi.org/10.1007/s00605-023-01843-0}, DOI={10.1007/s00605-023-01843-0}, abstractNote={We study the Q-Kostka polynomials $$L_{\lambda \mu }(t)$$ by the vertex operator realization of the Q-Hall–Littlewood functions $$G_{\lambda }(x;t)$$ and derive new formulae for $$L_{\lambda \mu }(t)$$ . In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials $$Y^{\lambda }_{\mu }(t)$$ as both an analogue of the Green polynomials and deformation of the spin irreducible characters of $$\mathfrak S_n$$ . Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of $$Y^{\lambda }_{\mu }(t)$$ are included for $$n\le 7.$$}, journal={MONATSHEFTE FUR MATHEMATIK}, author={Jiang, Anguo and Jing, Naihuan and Liu, Ning}, year={2023}, month={Mar} }
 @article{gao_jing_xia_zhang_2023, title={Quantum N-toroidal Algebras and Extended Quantized GIM Algebras of N-fold Affinization}, volume={2}, ISSN={["2194-671X"]}, url={https://doi.org/10.1007/s40304-022-00316-4}, DOI={10.1007/s40304-022-00316-4}, abstractNote={We introduce the notion of quantum N-toroidal algebras as natural generalization of the quantum toroidal algebras as well as extended quantized GIM algebras of N-fold affinization. We show that the quantum N-toroidal algebras are quotients of the extended quantized GIM algebras of N-fold affinization, which generalizes a well-known result of Berman and Moody for Lie algebras.}, journal={COMMUNICATIONS IN MATHEMATICS AND STATISTICS}, author={Gao, Yun and Jing, Naihuan and Xia, Limeng and Zhang, Honglian}, year={2023}, month={Feb} }
 @article{jing_liu_zhang_2023, title={Quantum algebra of multiparameter Manin matrices}, url={https://doi.org/10.1016/j.jalgebra.2023.06.002}, DOI={10.1016/j.jalgebra.2023.06.002}, abstractNote={Multiparametric quantum semigroups Mqˆ,pˆ(n) are generalization of the one-parameter general linear semigroups Mq(n), where qˆ=(qij) and pˆ=(pij) are 2n2 parameters satisfying certain conditions. In this paper, we study the algebra of multiparametric Manin matrices using the R-matrix method. The systematic approach enables us to obtain several classical identities such as Muir's identities, Newton's identities, Capelli-type identities, Cauchy-Binet's identity both for determinant and permanent as well as a rigorous proof of the MacMahon master equation for the quantum algebra of multiparametric Manin matrices. Some of the generalized identities are also lifted to multiparameter q-Yangians.}, journal={Journal of Algebra}, author={Jing, Naihuan and Liu, Yinlong and Zhang, Jian}, year={2023}, month={Jun} }
 @article{jing_zhang_liu_2023, title={R-matrix Presentation of Quantum Affine Algebra in Type A2n-1(2)}, volume={18}, ISSN={["2731-8656"]}, DOI={10.1007/s11464-021-0434-7}, abstractNote={In this paper, we give an RTT presentation of the twisted quantum affine algebra of type A 2−1 (2) and show that it is isomorphic to the Drinfeld new realization via the Gauss decomposition of the L-operators. This provides the first such presentation for twisted quantum affine algebras with nontrivial central elements.}, number={3}, journal={FRONTIERS OF MATHEMATICS}, author={Jing, Naihuan and Zhang, Xia and Liu, Ming}, year={2023}, month={May}, pages={513–564} }
 @article{ma_zhao_jing_2023, title={Separability and classification of multipartite quantum states}, volume={20}, ISSN={["1612-202X"]}, DOI={10.1088/1612-202X/ad0537}, abstractNote={We study separability in arbitrary multipartite quantum systems based on principal base matrices. Necessary conditions are presented for different kinds of separable states. These conditions can give a complete classification of multipartite quantum states. While the usual Bloch representation of a density matrix uses three types of generators, the representation with principal base matrices has one uniform type of generator which simplifies computation. In this paper, we take advantage of this simplicity to derive useful and operational criteria to detect multipartite separability. We first obtain criteria on detecting 1−3 separable, 2−2 separable, 1−1−2 separable and fully separable four-partite quantum states. We then study k-separability for multipartite quantum states in arbitrary dimensions. Detailed examples are given to show that our criteria are able to detect more entanglement states than some existing criteria.}, number={12}, journal={LASER PHYSICS LETTERS}, author={Ma, Pan-Wen and Zhao, Hui and Jing, Naihuan}, year={2023}, month={Dec} }
 @article{zhang_jing_fei_2023, title={Sharing quantum nonlocality in star network scenarios}, volume={18}, ISSN={["2095-0470"]}, DOI={10.1007/s11467-022-1242-6}, abstractNote={The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.}, number={3}, journal={FRONTIERS OF PHYSICS}, author={Zhang, Tinggui and Jing, Naihuan and Fei, Shao-Ming}, year={2023}, month={Jun} }
 @article{hu_jing_2023, title={Uncertainty relations for metric adjusted skew information and Cauchy-Schwarz inequality}, volume={20}, ISSN={["1612-202X"]}, url={https://doi.org/10.1088/1612-202X/accce3}, DOI={10.1088/1612-202X/accce3}, abstractNote={Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an in-depth investigation using the methodologies of sampling coordinates of observables and convex functions to refine the uncertainty relations in both the product form of two observables and summation form of multiple observables.}, number={8}, journal={LASER PHYSICS LETTERS}, author={Hu, Xiaoli and Jing, Naihuan}, year={2023}, month={Aug} }
 @article{chang_jing_zhang_2022, title={Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States}, volume={62}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-022-05267-8}, abstractNote={In this paper, we study the stochastic local operation and classical communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states by mode-n matricization of the coefficient tensors. We establish a new scheme of using the CANDECOMP/PARAFAC (CP) decomposition of tensors to find necessary and sufficient conditions between the mode-n unfolding and SLOCC&LU equivalence for pure multi-qudit states. For multipartite mixed states, we present a necessary and sufficient condition for LU equivalence and necessary condition for SLOCC equivalence.}, number={1}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Chang, Jingmei and Jing, Naihuan and Zhang, Tinggui}, year={2022}, month={Dec} }
 @article{jing_zhang_2022, title={Criteria of Genuine Multipartite Entanglement Based on Correlation Tensors}, volume={61}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-022-05253-0}, abstractNote={We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems.}, number={12}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Jing, Naihuan and Zhang, Meiming}, year={2022}, month={Dec} }
 @article{jing_kong_li_tan_2022, title={Deforming vertex algebras by vertex bialgebras}, volume={11}, ISSN={["1793-6683"]}, DOI={10.1142/S0219199722500675}, abstractNote={This is a continuation of a previous study initiated by one of us on nonlocal vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we study a notion of right $H$-comodule nonlocal vertex algebra for a nonlocal vertex bialgebra $H$ and give a construction of deformations of vertex algebras with a right $H$-comodule nonlocal vertex algebra structure and a compatible $H$-module nonlocal vertex algebra structure. We also give a construction of $\phi$-coordinated quasi modules for smash product nonlocal vertex algebras. As an example, we give a family of quantum vertex algebras by deforming the vertex algebras associated to non-degenerate even lattices.}, journal={COMMUNICATIONS IN CONTEMPORARY MATHEMATICS}, author={Jing, Naihuan and Kong, Fei and Li, Haisheng and Tan, Shaobin}, year={2022}, month={Nov} }
 @article{zhao_yang_jing_wang_fei_2022, title={Detection of Multipartite Entanglement Based on Heisenberg-Weyl Representation of Density Matrices}, volume={61}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-022-05123-9}, abstractNote={We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria.}, number={5}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Zhao, Hui and Yang, Yu and Jing, Naihuan and Wang, Zhi-Xi and Fei, Shao-Ming}, year={2022}, month={May} }
 @article{zhao_liu_jing_wang_2022, title={Detection of genuine entanglement for multipartite quantum states}, volume={21}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-022-03659-7}, abstractNote={We study genuine tripartite entanglement and multipartite entanglement of arbitrary $n$-partite quantum states by using the representations with generalized Pauli operators of a density matrices. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra $\mathfrak{su}(d)$, the representation with generalized Pauli operators has one uniformed type of generators and it simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more entangled states than previous methods as backed by detailed examples.}, number={9}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhao, Hui and Liu, Yu-Qiu and Jing, Naihuan and Wang, Zhi-Xi}, year={2022}, month={Sep} }
 @article{zhao_liu_fei_wang_jing_2022, title={Detection of genuine multipartite entanglement based on principal basis matrix representations}, volume={19}, ISSN={["1612-202X"]}, DOI={10.1088/1612-202X/ac50af}, abstractNote={We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.}, number={3}, journal={LASER PHYSICS LETTERS}, author={Zhao, Hui and Liu, Yu-Qiu and Fei, Shao-Ming and Wang, Zhi-Xi and Jing, Naihuan}, year={2022}, month={Mar} }
 @article{zhao_liu_jing_wang_fei_2022, title={Detection of genuine tripartite entanglement based on Bloch representation of density matrices}, volume={21}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-022-03456-2}, abstractNote={We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria.}, number={3}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhao, Hui and Liu, Yu-Qiu and Jing, Naihuan and Wang, Zhi-Xi and Fei, Shao-Ming}, year={2022}, month={Mar} }
 @article{hu_jing_2022, title={Improved unitary uncertainty relations}, volume={21}, ISSN={["1573-1332"]}, url={https://doi.org/10.1007/s11128-021-03396-3}, DOI={10.1007/s11128-021-03396-3}, abstractNote={We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy–Schwarz inequality using a method of brackets and convex functions. The unitary uncertainty relations outperform several strong unitary uncertainty relations, notably better than some recent best lower bounds such as [Phys. Rev. Lett. 120, 230402 (2018)] and [Phys. Rev. A. 100, 022116 (2019)].}, number={2}, journal={QUANTUM INFORMATION PROCESSING}, publisher={Springer Science and Business Media LLC}, author={Hu, Xiaoli and Jing, Naihuan}, year={2022}, month={Feb} }
 @article{huang_jing_2022, title={Lattice structure of modular vertex algebras}, volume={592}, ISSN={["1090-266X"]}, url={https://doi.org/10.1016/j.jalgebra.2021.10.030}, DOI={10.1016/j.jalgebra.2021.10.030}, abstractNote={In this paper we study the integral form of the lattice vertex algebra $V_L$. We show that divided powers of general vertex operators preserve the integral lattice spanned by Schur functions indexed by partition-valued functions. We also show that the Garland operators, counterparts of divided powers of Heisenberg elements in affine Lie algebras, also preserve the integral form. These construe analogs of the Kostant $\mathbb Z$-forms for the enveloping algebras of simple Lie algebras and the algebraic affine Lie groups in the situation of the lattice vertex algebras.}, journal={JOURNAL OF ALGEBRA}, publisher={Elsevier BV}, author={Huang, Haihua and Jing, Naihuan}, year={2022}, month={Feb}, pages={1–17} }
 @article{jing_wang_zhang_2022, title={Level-1/2 Realization of Quantum N-Toroidal Algebra in Type C-n}, volume={29}, ISSN={["0219-1733"]}, DOI={10.1142/S1005386722000074}, abstractNote={We construct a level -1/2 vertex representation of the quantum [Formula: see text]-toroidal algebra of type [Formula: see text], which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of the quantum toroidal algebra for type [Formula: see text] as a by-product.}, number={01}, journal={ALGEBRA COLLOQUIUM}, author={Jing, Naihuan and Wang, Qianbao and Zhang, Honglian}, year={2022}, month={Mar}, pages={79–98} }
 @article{chang_jing_2022, title={Local Unitary Equivalence of Generic Multi-qubits Based on the CP Decomposition}, volume={61}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-022-05106-w}, abstractNote={The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral decomposition of matrices to higher-order tensors. In this paper we use the CP decomposition to study unitary equivalence of higher order tensors and construct several invariants of local unitary equivalence for general higher order tensors. Based on this new method, we study the coefficient tensors of $3$-qubit states and obtain a necessary and sufficient criterion for local unitary equivalence of general tripartite states in terms of the CP decomposition. We also generalize this method to obtain some invariants of local unitary equivalence for general multi-partite qudits.}, number={5}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Chang, Jingmei and Jing, Naihuan}, year={2022}, month={May} }
 @article{zhang_jing_zhao_2022, title={Monogamy and Polygamy Relations of Quantum Correlations for Multipartite Systems}, volume={61}, ISSN={["1572-9575"]}, url={https://doi.org/10.1007/s10773-022-04971-9}, DOI={10.1007/s10773-022-04971-9}, abstractNote={We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the monogamy inequality of the α th $\left (0\leq \alpha \leq \frac {r}{2}, r\geq 2\right )$ power of concurrence for any 2 ⊗ 2 ⊗ 2n− 2 tripartite states and generalize it to the n-qubit quantum states. In addition to concurrence, we show that the monogamy relations are satisfied by other quantum correlation measures such as entanglement of formation. Moreover, the polygamy inequality of the β th (β ≤ 0) power of concurrence and the β th (β ≥ s, 0 ≤ s ≤ 1) power of the negativity are presented for 2 ⊗ 2 ⊗ 2n− 2. We then obtain the polygamy inequalities of quantum correlations for multipartite states. Finally, our results are shown to be tighter than previous studies using detailed examples.}, number={1}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, publisher={Springer Science and Business Media LLC}, author={Zhang, Mei-Ming and Jing, Naihuan and Zhao, Hui}, year={2022}, month={Jan} }
 @article{xiao_jing_yu_fei_li-jost_2022, title={Near-Optimal Variance-Based Uncertainty Relations}, volume={10}, ISSN={["2296-424X"]}, DOI={10.3389/fphy.2022.846330}, abstractNote={Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg’s uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum theory. Aside from its fundamental significance, the mathematical characterization of this restriction, known as ‘uncertainty relation’, plays important roles in a wide range of applications, stimulating the formation of tighter uncertainty relations. In this work, we investigate the fundamental limitations of variance-based uncertainty relations, and introduce several ‘near optimal’ bounds for incompatible observables. Our results consist of two morphologically distinct phases: lower bounds that illustrate the uncertainties about measurement outcomes, and the upper bound that indicates the potential knowledge we can gain. Combining them together leads to an uncertainty interval, which captures the essence of uncertainties in quantum theory. Finally, we have detailed how to formulate lower bounds for product-form variance-based uncertainty relations by employing entropic uncertainty relations, and hence built a link between different forms of uncertainty relations.}, journal={FRONTIERS IN PHYSICS}, author={Xiao, Yunlong and Jing, Naihuan and Yu, Bing and Fei, Shao-Ming and Li-Jost, Xianqing}, year={2022}, month={Apr} }
 @article{jing_zhang_2022, title={On Hopf algebraic structures of quantum toroidal algebras}, volume={10}, ISSN={["1532-4125"]}, DOI={10.1080/00927872.2022.2127604}, abstractNote={ABSTRACT We define an algebra using a simplified set of generators for the quantum toroidal algebra and show that there exists an epimorphism from to . We derive a closed formula of the comultiplication on the generators of that extends that of the quantum affine algebra . As a consequence, we show that is a Hopf algebra for n = 1, 2 and give conjectural formulas in the general case. We further show that is isomorphic to a double algebra.}, journal={COMMUNICATIONS IN ALGEBRA}, author={Jing, Naihuan and Zhang, Honglian}, year={2022}, month={Oct} }
 @article{boulware_jing_misra_2022, title={On Smith normal forms of q-Varchenko matrices}, volume={34}, ISSN={["2415-721X"]}, DOI={10.12958/adm2006}, abstractNote={In this paper, we investigate q-Varchenko matrices for some hyperplane arrangements with symmetry in two andthree dimensions, and prove that they have a Smith normal formover Z[q]. In particular, we examine the hyperplane arrangement forthe regular n-gon in the plane and the dihedral model in the spaceand Platonic polyhedra. In each case, we prove that the q-Varchenko matrix associated with the hyperplane arrangement has a Smith normal form over Z[q] and realize their congruent transformation matrices over Z[q] as well.}, number={2}, journal={ALGEBRA AND DISCRETE MATHEMATICS}, author={Boulware, N. and Jing, N. and Misra, K. C.}, year={2022}, pages={187–222} }
 @article{zhao_liu_wang_jing_li_2022, title={On genuine entanglement for tripartite systems}, volume={20}, ISSN={["1793-6918"]}, DOI={10.1142/S0219749921500386}, abstractNote={In this paper, we investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit states combining with the partial transposition of the density matrices. Then, we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples, our results are seen to be able to detect more genuine tripartite entangled states than previous studies.}, number={02}, journal={INTERNATIONAL JOURNAL OF QUANTUM INFORMATION}, author={Zhao, Hui and Liu, Lin and Wang, Zhi-Xi and Jing, Naihuan and Li, Jing}, year={2022}, month={Mar} }
 @article{jing_liu_2022, title={On irreducible characters of the Iwahori-Hecke algebra in type A}, volume={598}, ISSN={["1090-266X"]}, url={https://doi.org/10.1016/j.jalgebra.2022.01.020}, DOI={10.1016/j.jalgebra.2022.01.020}, abstractNote={In this paper, we use vertex operators to compute irreducible characters of the Iwahori-Hecke algebra of type A. Two general formulas are given for the irreducible characters in terms of those of the symmetric groups or the Iwahori-Hecke algebras in lower degrees. Explicit formulas are derived for the irreducible characters labeled by hooks and two-row partitions. We also formulate a determinant type Murnaghan-Nakayama formula and give another proof of the combinatorial Murnaghan-Nakayama rule. As applications, we study super-characters of the Iwahori-Hecke algebra as well as the bitrace of the regular representation and provide a simple proof of the Halverson-Leduc-Ram formula.}, journal={JOURNAL OF ALGEBRA}, publisher={Elsevier BV}, author={Jing, Naihuan and Liu, Ning}, year={2022}, month={May}, pages={24–47} }
 @article{chen_jing_kong_tan_2022, title={On quantum toroidal algebra of type A(1)}, volume={226}, ISSN={["1873-1376"]}, DOI={10.1016/j.jpaa.2021.106814}, abstractNote={In this paper we introduce a new quantum algebra which specializes to the 2-toroidal Lie algebra of type A1. We prove that this quantum toroidal algebra has a natural triangular decomposition, a (topological) Hopf algebra structure and a vertex operator realization.}, number={1}, journal={JOURNAL OF PURE AND APPLIED ALGEBRA}, author={Chen, Fulin and Jing, Naihuan and Kong, Fei and Tan, Shaobin}, year={2022}, month={Jan} }
 @article{liu_hu_jing_2022, title={Quantum Supergroup U-r,U-s(osp(1,2)), Scasimir operators and Dickson polynomials}, volume={10}, ISSN={["1793-6829"]}, url={https://doi.org/10.1142/S0219498824500038}, DOI={10.1142/S0219498824500038}, abstractNote={A BSTRACT . We study the center of the two-parameter quantum supergroup U r,s ( osp (1 , 2)) using the Dickson polynomial. We show that the Scasimir operator is completely determined by the q deformed Chebychev polynomial, generalizing an earlier work of Arnaudon and Bauer.}, journal={JOURNAL OF ALGEBRA AND ITS APPLICATIONS}, author={Liu, Fu and Hu, Naihong and Jing, Naihuan}, year={2022}, month={Oct} }
 @article{zhou_hu_jing_2022, title={Quantum discords of tripartite quantum systems}, volume={21}, ISSN={["1573-1332"]}, url={https://doi.org/10.1007/s11128-022-03490-0}, DOI={10.1007/s11128-022-03490-0}, abstractNote={The quantum discord of bipartite systems is one of the best-known measures of non-classical correlations and an important quantum resource. In the recent work appeared in [Phys. Rev. Lett 2020, 124:110401], the quantum discord has been generalized to multipartite systems. In this paper, we give analytic solutions of the quantum discord for tripartite states with fourteen parameters.}, number={4}, journal={QUANTUM INFORMATION PROCESSING}, publisher={Springer Science and Business Media LLC}, author={Zhou, Jianming and Hu, Xiaoli and Jing, Naihuan}, year={2022}, month={Apr} }
 @article{zhang_jing_fei_2022, title={Quantum separability criteria based on realignment moments}, volume={21}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-022-03630-6}, abstractNote={Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented in [Phys. Rev. Lett. 125, 200501 (2020)] by Elben et al. based on the first three partially transposed (PT) moments of density matrices. Then in [Phys. Rev. Lett. 127, 060504 (2021)] Yu \emph{et al.} proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement.}, number={8}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhang, Tinggui and Jing, Naihuan and Fei, Shao-Ming}, year={2022}, month={Aug} }
 @article{huang_zhang_zhao_jing_2022, title={Separability Criteria Based on the Weyl Operators}, volume={24}, ISSN={["1099-4300"]}, url={https://doi.org/10.3390/e24081064}, DOI={10.3390/e24081064}, abstractNote={Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.}, number={8}, journal={ENTROPY}, author={Huang, Xiaofen and Zhang, Tinggui and Zhao, Ming-Jing and Jing, Naihuan}, year={2022}, month={Aug} }
 @article{chen_jing_kong_tan_2022, title={TWISTED QUANTUM AFFINIZATIONS AND QUANTIZATION OF EXTENDED AFFINE LIE ALGEBRAS}, volume={10}, ISSN={["1088-6850"]}, DOI={10.1090/tran/8706}, abstractNote={In this paper, for an arbitrary Kac-Moody Lie algebra $\mathfrak{g}$ and a diagram automorphism $\mu$ of $\mathfrak{g}$ satisfying two linking conditions, we introduce and study a $\mu$-twisted quantum affinization algebra $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$ of $\mathfrak{g}$. When $\mathfrak{g}$ is of finite type, $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$ is Drinfeld's current algebra realization of the twisted quantum affine algebra. And, when $\mu=\mathrm{Id}$, $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$ is the quantum affinization algebra introduced by Ginzburg-Kapranov-Vasserot. As the main results of this paper, we first prove a triangular decomposition of $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$. Second, we give a simple characterization of the affine quantum Serre relations on restricted $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$-modules in terms of "normal order products". Third, we prove that the category of restricted $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$-modules is a monoidal category and hence obtain a topological Hopf algebra structure on the "restricted completion" of $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$. Fourth, we study the classical limit of $\mathcal{U}_{\hbar}(\hat{\mathfrak{g}}_\mu)$ and abridge it to the quantization theory of extended affine Lie algebras. In particular, based on a classification result of Allison-Berman-Pianzola, we obtain the $\hbar$-deformation of nullity $2$ extended affine Lie algebras.}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Chen, Fulin and Jing, Naihuan and Kong, Fei and Tan, Shaobin}, year={2022}, month={Oct} }
 @article{jing_liu_2022, title={The Green polynomials via vertex operators}, volume={226}, ISSN={["1873-1376"]}, DOI={10.1016/j.jpaa.2022.107032}, abstractNote={An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Green's polynomials associated with upper partitions of length $\leq 3$ and the diagonal lengths $\leq 3$; (3) a Murnaghan-Nakayama type formula for the Green polynomial is obtained; and (4) an iterative formula is derived for the bitrace of the finite general linear group $G$ and the Iwahori-Hecke algebra of type $A$ on the permutation module of $G$ by its Borel subgroup.}, number={8}, journal={JOURNAL OF PURE AND APPLIED ALGEBRA}, author={Jing, Naihuan and Liu, Ning}, year={2022}, month={Aug} }
 @article{zhang_jing_zhao_2022, title={Tightening monogamy and polygamy relations of unified entanglement in multipartite systems}, volume={21}, ISSN={["1573-1332"]}, url={https://doi.org/10.1007/s11128-022-03479-9}, DOI={10.1007/s11128-022-03479-9}, abstractNote={We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polygamy inequalities of the $\beta$th ($\beta\geq \max\{1, s\}, 0\leq s\leq s_0, 0\leq s_0\leq\sqrt{2}$) power of the entanglement of formation for $2\otimes2\otimes2$ and $n$-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies.}, number={4}, journal={QUANTUM INFORMATION PROCESSING}, publisher={Springer Science and Business Media LLC}, author={Zhang, Mei-Ming and Jing, Naihuan and Zhao, Hui}, year={2022}, month={Mar} }
 @article{zhang_jing_2022, title={Tighter monogamy relations of entanglement measures based on fidelity}, volume={19}, ISSN={["1612-202X"]}, DOI={10.1088/1612-202X/ac772e}, abstractNote={We study the Bures measure of entanglement and the geometric measure of entanglement as special cases of entanglement measures based on fidelity, and find their tighter monogamy inequalities over tri-qubit systems as well as multi-qubit systems. Furthermore, we derive the monogamy inequality of concurrence for qudit quantum systems by projecting higher-dimensional states to qubit substates.}, number={8}, journal={LASER PHYSICS LETTERS}, author={Zhang, Meiming and Jing, Naihuan}, year={2022}, month={Aug} }
 @article{luo_zhang_huang_jing_2022, title={Two Quantum Proxy Blind Signature Schemes Based on Controlled Quantum Teleportation}, volume={24}, ISSN={["1099-4300"]}, url={https://doi.org/10.3390/e24101421}, DOI={10.3390/e24101421}, abstractNote={We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted in a two-way form between the same sender and receiver via a five-qubit cluster state. One-way hash functions, Bell-state measurements, and unitary operations are adopted in these two schemes. Our schemes use the physical characteristics of quantum mechanics to implement delegation, signature, and verification processes. Moreover, a quantum key distribution protocol and a one-time pad are adopted in these schemes.}, number={10}, journal={ENTROPY}, author={Luo, Qiming and Zhang, Tinggui and Huang, Xiaofen and Jing, Naihuan}, year={2022}, month={Oct} }
 @article{jing_kong_li_tan_2021, title={(G,χ)-equivariant ϕ-coordinated quasi modules for nonlocal vertex algebras}, volume={570}, url={https://doi.org/10.1016/j.jalgebra.2020.11.013}, DOI={10.1016/j.jalgebra.2020.11.013}, abstractNote={In this paper, we study (G,χϕ)-equivariant ϕ-coordinated quasi modules for nonlocal vertex algebras. Among the main results, we establish several conceptual results, including a generalized commutator formula and a general construction of weak quantum vertex algebras and their (G,χϕ)-equivariant ϕ-coordinated quasi modules. As an application, we also construct (equivariant) ϕ-coordinated quasi modules for lattice vertex algebras by using Lepowsky's work on twisted vertex operators.}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Jing, Naihuan and Kong, Fei and Li, Haisheng and Tan, Shaobin}, year={2021}, month={Mar}, pages={24–74} }
 @article{bryan_jing_2021, title={An iterative formula for the Kostka-Foulkes polynomials}, volume={54}, ISSN={["1572-9192"]}, url={https://doi.org/10.1007/s10801-021-01018-w}, DOI={10.1007/s10801-021-01018-w}, abstractNote={An iterative formula for the Kostka–Foulkes polynomials is given using the vertex operator realization of the Hall–Littlewood polynomials. The operational formula can handle large Kostka–Foulkes polynomials, and a stability property for the Kostka–Foulkes polynomials is shown. We also use our algorithm to give a formula of $$K_{\lambda \mu }(t)$$ for $$\mu $$ being hook-shaped.}, number={2}, journal={JOURNAL OF ALGEBRAIC COMBINATORICS}, publisher={Springer Science and Business Media LLC}, author={Bryan, Timothee W. and Jing, Naihuan}, year={2021}, month={Sep}, pages={625–634} }
 @article{jing_mangum_misra_2021, title={Fermionic realization of twisted toroidal Lie algebras}, volume={20}, ISSN={["1793-6829"]}, url={https://doi.org/10.1142/S0219498821501437}, DOI={10.1142/S0219498821501437}, abstractNote={In this paper, we construct a fermionic realization of the twisted toroidal Lie algebra of type [Formula: see text] and [Formula: see text] based on the newly found Moody–Rao–Yokonuma-like presentation.}, number={08}, journal={JOURNAL OF ALGEBRA AND ITS APPLICATIONS}, publisher={World Scientific Pub Co Pte Lt}, author={Jing, Naihuan and Mangum, Chad R. and Misra, Kailash C.}, year={2021}, month={Aug} }
 @article{jing_wang_zhang_2021, title={Poincare Series of Relative Symmetric Invariants for SLn(C)}, volume={24}, ISSN={["1572-9079"]}, DOI={10.1007/s10468-020-09962-0}, abstractNote={Let (N, G), where N is a normal subgroup of G<SL_n(C), be a pair of finite groups and V a finite-dimensional fundamental G-module. We study the G-invariants in the symmetric algebra S(V) by giving explicit formulas of the Poincar\'{e} series for the induced modules and restriction modules. In particular, this provides a uniform formula of the Poincar\'{e} series for the symmetric invariants in terms of the McKay-Slodowy correspondence. Moreover, we also derive a global version of the Poincar\'e series in terms of Tchebychev polynomials in the sense that one needs only the dimensions of the subgroups and their group-types to completely determine the Poincar\'e series.}, number={3}, journal={ALGEBRAS AND REPRESENTATION THEORY}, author={Jing, Naihuan and Wang, Danxia and Zhang, Honglian}, year={2021}, month={Jun}, pages={601–623} }
 @article{chen_jing_kong_tan_2021, title={Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation}, volume={64}, ISSN={["1869-1862"]}, DOI={10.1007/s11425-019-1615-x}, abstractNote={Let $\fg$ be an affine Kac-Moody algebra, and $\mu$ a diagram automorphism of $\fg$. In this paper, we give an explicit realization for the universal central extension $\wh\fg[\mu]$ of the twisted loop algebra of $\fg$ related to $\mu$, which provides a Moody-Rao-Yokonuma presentation for the algebra $\wh\fg[\mu]$ when $\mu$ is non-transitive, and the presentation is indeed related to the quantization of toroidal Lie algebras.}, number={6}, journal={SCIENCE CHINA-MATHEMATICS}, author={Chen, Fulin and Jing, Naihuan and Kong, Fei and Tan, Shaobin}, year={2021}, month={Jun}, pages={1181–1200} }
 @article{jing_xu_zhang_2021, title={Vertex representations of quantum N-toroidal algebras for type C}, volume={20}, ISSN={["1793-6829"]}, DOI={10.1142/S0219498821501851}, abstractNote={Quantum [Formula: see text]-toroidal algebras are generalizations of quantum affine algebras and quantum toroidal algebras. In this paper, we construct a level-one vertex representation of the quantum [Formula: see text]-toroidal algebra for type [Formula: see text]. In particular, we also obtain a level-one module of the quantum toroidal algebra for type [Formula: see text] as a special case.}, number={10}, journal={JOURNAL OF ALGEBRA AND ITS APPLICATIONS}, author={Jing, Naihuan and Xu, Zhucheng and Zhang, Honglian}, year={2021}, month={Oct} }
 @article{jing_li_cai_2020, title={Correlation functions of charged free boson and fermion systems}, volume={2020}, ISSN={["1742-5468"]}, DOI={10.1088/1742-5468/aba0aa}, abstractNote={Using the idea of the quantum inverse scattering method, we introduce the operators B(x), C(x) and B̃(x),C̃(x) corresponding to the off-diagonal entries of the monodromy matrix T for the phase model and i-boson model in terms of bc fermions and neutral fermions respectively, thus giving alternative treatment of the KP and BKP hierarchies. We also introduce analogous operators B*(x) and C*(x) for the charged free boson system and show that they are in complete analogy to those of bc fermionic fields. It is proved that the correlation function ⟨0|C(xN)⋯C(x1)B(y1)⋯B(yN)|0⟩ in the bc fermionic fields is the inverse of the correlation function ⟨0|C*(xN)⋯C*(x1)B*(y1)⋯B*(yN)|0⟩ in the charged free bosons.}, number={8}, journal={JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT}, author={Jing, Naihuan and Li, Zhijun and Cai, Tommy Wuxing}, year={2020}, month={Aug} }
 @article{chen_jing_kong_tan_2020, title={DRINFELD-TYPE PRESENTATIONS OF LOOP ALGEBRAS}, volume={373}, ISSN={["1088-6850"]}, DOI={10.1090/tran/8120}, abstractNote={Let $\mathfrak{g}$ be the derived subalgebra of a Kac-Moody Lie algebra of finite type or affine type, $\mu$ a diagram automorphism of $\mathfrak{g}$ and $L(\mathfrak{g},\mu)$ the loop algebra of $\mathfrak{g}$ associated to $\mu$. In this paper, by using the vertex algebra technique, we provide a general construction of current type presentations for the universal central extension $\widehat{\mathfrak{g}}[\mu]$ of $L(\mathfrak{g},\mu)$. The construction contains the classical limit of Drinfeld's new realization for (twisted and untwisted) quantum affine algebras ([Dr]) and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras ([MRY]) as special examples. As an application, when $\mathfrak{g}$ is of simply-laced type, we prove that the classical limit of the $\mu$-twisted quantum affinization of the quantum Kac-Moody algebra associated to $\mathfrak{g}$ introduced in [CJKT1] is the universal enveloping algebra of $\widehat{\mathfrak{g}}[\mu]$.}, number={11}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Chen, Fulin and Jing, Naihuan and Kong, Fei and Tan, Shaobin}, year={2020}, month={Nov}, pages={7713–7753} }
 @article{cai_jing_2020, title={Deformation of Cayley's hyperdeterminants}, volume={27}, ISSN={["1077-8926"]}, DOI={10.37236/8091}, abstractNote={We introduce a deformation of Cayley's second hyperdeterminant for even-dimensional hypermatrices. As an application, we obtain a generalization of Jacobi-Trudi formula for Macdonald functions of rectangular shapes generalizing Matsumoto's formula for Jack functions.}, number={2}, journal={ELECTRONIC JOURNAL OF COMBINATORICS}, author={Cai, Tommy Wuxing and Jing, Naihuan}, year={2020}, month={Jun} }
 @article{jing_liu_molev_2020, title={Isomorphism between the R-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types B and D}, volume={16}, ISSN={["1815-0659"]}, DOI={10.3842/SIGMA.2020.043}, abstractNote={Following the approach of Ding and Frenkel [Comm. Math. Phys. 156 (1993), 277–300] for type A, we showed in our previous work [J. Math. Phys. 61 (2020), 031701, 41 pages] that the Gauss decomposition of the generator matrix in the R-matrix presentation of the quantum affine algebra yields the Drinfeld generators in all classical types. Complete details for type C were given therein, while the present paper deals with types B and D. The arguments for all classical types are quite similar so we mostly concentrate on necessary additional details specific to the underlying orthogonal Lie algebras.}, journal={SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS}, author={Jing, Naihuan and Liu, Ming and Molev, Alexander}, year={2020} }
 @article{jing_liu_molev_2020, title={Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C}, volume={61}, ISSN={["1089-7658"]}, url={https://doi.org/10.1063/1.5133854}, DOI={10.1063/1.5133854}, abstractNote={An explicit isomorphism between the R-matrix and Drinfeld presentations of the quantum affine algebra in type A was given by Ding and Frenkel [Commun. Math. Phys. 156, 277–300 (1993)]. We show that this result can be extended to types B, C, and D and give a detailed construction for type C in this paper. In all classical types, the Gauss decomposition of the generator matrix in the R-matrix presentation yields the Drinfeld generators. To prove that the resulting map is an isomorphism, we follow the work of Frenkel and Mukhin [Sel. Math. 8, 537–635 (2002)] in type A and employ the universal R-matrix to construct the inverse map. A key role in our construction is played by a homomorphism theorem, which relates the quantum affine algebra of rank n − 1 in the R-matrix presentation with a subalgebra of the corresponding algebra of rank n of the same type.}, number={3}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Liu, Ming and Molev, Alexander}, year={2020}, month={Mar} }
 @article{jing_wang_zhang_2020, title={Poincare series, exponents of affine Lie algebras, and McKay-Slodowy correspondence}, volume={546}, ISSN={["1090-266X"]}, url={https://doi.org/10.1016/j.jalgebra.2019.10.042}, DOI={10.1016/j.jalgebra.2019.10.042}, abstractNote={Let N be a normal subgroup of a finite group G and V a fixed finite-dimensional G-module. The Poincaré series for the multiplicities of induced modules and restriction modules in the tensor algebra T(V)=⊕k≥0V⊗k are studied in connection with the McKay-Slodowy correspondence. In particular, it is shown that the closed formulas for the Poincaré series associated with the distinguished pairs of subgroups of SU2 give rise to the exponents of all untwisted and twisted affine Lie algebras except A2n(1).}, journal={JOURNAL OF ALGEBRA}, publisher={Elsevier BV}, author={Jing, Naihuan and Wang, Danxia and Zhang, Honglian}, year={2020}, month={Mar}, pages={135–162} }
 @article{zhou_hu_jing_2020, title={Quantum Discord of Certain Two-Qubit States}, volume={59}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-019-04333-y}, abstractNote={Quantum discord is an effective measure of quantum correlation introduced by Olliver and Zurek. We evaluate analytically the quantum discord for a large family of non-X-states. Exact solutions of the quantum discord are obtained for four parametric spaces of non-X-states. Dynamic behavior of the quantum discord is also explored under the action of the Kraus operator.}, number={2}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Zhou, Jianming and Hu, Xiaoli and Jing, Naihuan}, year={2020}, month={Feb}, pages={415–425} }
 @article{jing_liu_molev_2020, title={Representations of Quantum Affine Algebras in their R-Matrix Realization}, volume={16}, ISSN={["1815-0659"]}, DOI={10.3842/SIGMA.2020.145}, abstractNote={We use the isomorphisms between the R-matrix and Drinfeld presentations of the quantum affine algebras in types B, C and D produced in our previous work to describe finite-dimensional irreducible representations in the R-matrix realization.We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the R-matrix and Drinfeld presentations of the Yangians.}, journal={SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS}, author={Jing, Naihuan and Liu, Ming and Molev, Alexander}, year={2020} }
 @article{zhao_zhang_jing_wang_2020, title={Separability criteria based on Bloch representation of density matrices}, volume={19}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-019-2504-2}, abstractNote={We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for separability under partition of tripartite and four-partite quantum states. Moreover, based on the norms of the correlation tensors,we obtain the separability criteria by matrix method. Using detailed examples, our results are seen to be able to detect more entangled states than previous studies. Finally, necessary conditions of separability for multipartite systems are given under arbitrary partition.}, number={1}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhao, Hui and Zhang, Mei-Ming and Jing, NaiHuan and Wang, Zhi-Xi}, year={2020}, month={Jan} }
 @article{jing_li_2020, title={Tau functions of the charged free bosons}, volume={63}, ISSN={["1869-1862"]}, DOI={10.1007/s11425-019-1735-4}, abstractNote={We study bosonic tau functions in relation with the charged free bosonic fields. It is proved that up to a constant the only tau function in the Fock space ℳ is the vacuum vector, and some tau functions are given in the completion $$\widetilde{\cal M}$$ by using Schur functions. We also give a new proof of Borchardt’s identity and obtain several q-series identities by using the boson-boson correspondence.}, number={11}, journal={SCIENCE CHINA-MATHEMATICS}, author={Jing, Naihuan and Li, Zhijun}, year={2020}, month={Nov}, pages={2157–2176} }
 @article{sun_fei_jing_li-jost_2020, title={Time optimal control based on classification of quantum gates}, volume={19}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-020-2602-1}, abstractNote={We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimal time problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases.}, number={3}, journal={QUANTUM INFORMATION PROCESSING}, author={Sun, Bao-Zhi and Fei, Shao-Ming and Jing, Naihuan and Li-Jost, Xianqing}, year={2020}, month={Feb} }
 @article{huang_zhang_jing_2020, title={Uncertainty relations based on Wigner-Yanase skew information}, volume={72}, ISSN={["1572-9494"]}, DOI={10.1088/1572-9494/ab892f}, abstractNote={In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner–Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds. We then propose new weighted uncertainty relations for two noncompatible observables. Two separable criteria via skew information are also obtained.}, number={7}, journal={COMMUNICATIONS IN THEORETICAL PHYSICS}, author={Huang, Xiaofen and Zhang, Tinggui and Jing, Naihuan}, year={2020}, month={Jul} }
 @article{jing_yang_liu_2020, title={Yangian doubles of classical types and their vertex representations}, url={https://doi.org/10.1063/1.5094058}, DOI={10.1063/1.5094058}, abstractNote={The Yangian double $DY(g_N)$ is introduced for the classical types of $g_N=so_{2n+1}$, $sp_{2n}$, $so_{2n}$. Via Gauss decomposition of the generator matrix, the Yangian double is given the Drinfeld presentation. In addition, bosonization of level $1$ realizations for the Yangian double $DY(g_N)$ of non-simply-laced types are explicitly constructed.}, journal={Journal of Mathematical Physics}, author={Jing, Naihuan and Yang, Fan and Liu, Ming}, year={2020}, month={May} }
 @article{zhao_zhao_jing_fei_2019, title={Detection of Genuine Multipartite Entanglement in Multipartite Systems}, volume={58}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-019-04193-6}, abstractNote={We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary multipartite systems.}, number={10}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Zhao, Jing Yun and Zhao, Hui and Jing, Naihuan and Fei, Shao-Ming}, year={2019}, month={Oct}, pages={3181–3191} }
 @article{yu_jing_li-jost_2019, title={Distribution of spin correlation strengths in multipartite systems}, volume={18}, ISSN={["1573-1332"]}, url={https://doi.org/10.1007/s11128-019-2458-4}, DOI={10.1007/s11128-019-2458-4}, abstractNote={For a two-qubit state, the isotropic strength measures the degree of isotropic spin correlation. The concept of isotropic strength is generalized to multipartite qudit systems, and the strength distributions for tripartite and quadripartite qudit systems are thoroughly investigated. We show that the sum of relative isotropic strengths of any three-qudit state over d-dimensional Hilbert space cannot exceed $$d-1$$ , which generalizes the case $$d=2$$ . The trade-off relations and monogamy-like relations of the sum of spin correlation strengths for pure three- and four-partite systems are derived. Moreover, the bounds of spin correlation strengths among different subsystems of a quadripartite state are used to analyze quantum entanglement.}, number={11}, journal={QUANTUM INFORMATION PROCESSING}, publisher={Springer Science and Business Media LLC}, author={Yu, Bing and Jing, Naihuan and Li-Jost, Xianqing}, year={2019}, month={Nov} }
 @article{xiao_guo_meng_jing_yung_2019, title={Incompatibility of observables as state-independent bound of uncertainty relations}, volume={100}, ISSN={["2469-9934"]}, DOI={10.1103/PhysRevA.100.032118}, abstractNote={For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here we explore one possible route towards this goal through Heisenberg's uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we quantify the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, but not on the quantum state. To justify our case, we focus on the incompatibility of spin systems. For an arbitrary setting of two or three linearly-independent Pauli-spin operators, the incompatibility is analytically solved, the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, the measure of incompatibility represents a versatile tool for applications such as testing entanglement of bipartite states, and EPR-steering criteria.}, number={3}, journal={PHYSICAL REVIEW A}, author={Xiao, Yunlong and Guo, Cheng and Meng, Fei and Jing, Naihuan and Yung, Man-Hong}, year={2019}, month={Sep} }
 @article{li_tang_jing_gu_2019, title={LOCC Distinguishable Orthogonal Product States with Least Entanglement Resource}, volume={58}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-019-04140-5}, abstractNote={In this paper, we construct 2n − 1 locally indistinguishable orthogonal product states in $$ {\mathbb{C}}^n\otimes {\mathbb{C}}^4\kern1em \left(n>4\right) $$ and $$ {\mathbb{C}}^n\otimes {\mathbb{C}}^5\kern1em \left(n\ge 5\right) $$ respectively. Moreover, a set of locally indistinguishable orthogonal product states with 2(n + 2l) − 8 elements in $$ {\mathbb{C}}^n\otimes {\mathbb{C}}^{2l}\kern1em \left(n\ge 2l>4\right) $$ and a class of locally indistinguishable orthogonal product states with 2(n + 2k + 1) − 7 elements in $$ {\mathbb{C}}^n\otimes {\mathbb{C}}^{2k+1}\kern1em \left(n\ge 2k+1>5\right) $$ are also constructed respectively. These classes of quantum states are then shown to be distinguishable by local operation and classical communication (LOCC) using a suitable $$ {\mathbb{C}}^2\otimes {\mathbb{C}}^2 $$ maximally entangled state respectively.}, number={8}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Li, Haiquan and Tang, Xilin and Jing, Naihuan and Gu, Ze}, year={2019}, month={Aug}, pages={2497–2509} }
 @article{jing_liu_2019, title={ON FUSION PROCEDURE FOR THE TWO-PARAMETER QUANTUM ALGEBRA IN TYPE A}, volume={14}, ISSN={["2304-7895"]}, DOI={10.21915/BIMAS.2019102}, abstractNote={Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(\mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and combinatorial description of the Schur-Weyl duality for the two-parameter quantum linear algebras of type $A$.}, number={1}, journal={BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES}, author={Jing, Naihuan and Liu, Ming}, year={2019}, month={Mar}, pages={15–29} }
 @article{wang_gao_jing_2019, title={On multivariable Zassenhaus formula}, volume={14}, ISSN={["1673-3576"]}, DOI={10.1007/s11464-019-0760-1}, abstractNote={We give a recursive algorithm to compute the multivariable Zassenhaus formula $${e^{{X_1} + {X_2} + \cdots + {X_n}}} = {e^{{X_1}}}{e^{{X_2}}} \ldots {e^{{X_n}}}\prod{_{k=2}^\infty}e^W{_k}$$ and derive an effective recursion formula of Wk.}, number={2}, journal={FRONTIERS OF MATHEMATICS IN CHINA}, author={Wang, Linsong and Gao, Yun and Jing, Naihuan}, year={2019}, month={Apr}, pages={421–433} }
 @article{fan_zhou_hu_jing_2019, title={Quantum Circuit Realization of Morphological Gradient for Quantum Grayscale Image}, volume={58}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-018-3943-8}, number={2}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Fan, Ping and Zhou, Ri-Gui and Hu, WenWen and Jing, Naihuan}, year={2019}, month={Feb}, pages={415–435} }
 @article{fan_zhou_hu_jing_2019, title={Quantum image edge extraction based on Laplacian operator and zero-cross method}, volume={18}, ISSN={1570-0755 1573-1332}, url={http://dx.doi.org/10.1007/S11128-018-2129-X}, DOI={10.1007/S11128-018-2129-X}, number={1}, journal={Quantum Information Processing}, publisher={Springer Science and Business Media LLC}, author={Fan, Ping and Zhou, Ri-Gui and Hu, Wen Wen and Jing, NaiHuan}, year={2019}, month={Jan} }
 @article{fan_zhou_hu_jing_2019, title={Quantum image edge extraction based on classical Sobel operator for NEQR}, volume={18}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-018-2131-3}, number={1}, journal={QUANTUM INFORMATION PROCESSING}, author={Fan, Ping and Zhou, Ri-Gui and Hu, Wenwen and Jing, Naihuan}, year={2019}, month={Jan} }
 @article{yu_jing_li-jost_2019, title={Strong unitary uncertainty relations}, volume={100}, ISSN={["2469-9934"]}, DOI={10.1103/PhysRevA.100.022116}, abstractNote={In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in [Phys. Rev. Lett. 120, 230402 (2018)] to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims.}, number={2}, journal={PHYSICAL REVIEW A}, author={Yu, Bing and Jing, Naihuan and Li-Jost, Xianqing}, year={2019}, month={Aug} }
 @article{butorac_jing_kozic_2019, title={h-Adic quantum vertex algebras associated with rational R-matrix in types B, C and D}, volume={109}, ISSN={["1573-0530"]}, DOI={10.1007/s11005-019-01199-3}, abstractNote={We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the Etingof--Kazhdan's construction in type $A$. Next, we construct the algebraically independent generators of the center of the $h$-adic quantum vertex algebra in type $B$ at the critical level, as well as the families of central elements in types $C$ and $D$. Finally, as an application, we obtain commutative subalgebras of the dual Yangian and the families of central elements of the appropriately completed double Yangian at the critical level, in types $B$, $C$ and $D$.}, number={11}, journal={LETTERS IN MATHEMATICAL PHYSICS}, author={Butorac, Marijana and Jing, Naihuan and Kozic, Slaven}, year={2019}, month={Nov}, pages={2439–2471} }
 @article{jing_xu_2018, title={Bosonic vertex representations of the toroidal superalgebras in type D(m, n)}, volume={17}, ISSN={["1793-6829"]}, DOI={10.1142/s0219498818500573}, abstractNote={In this paper, vertex representations of the 2-toroidal Lie superalgebras of type D(m,n) are constructed using both bosonic fields and vertex operators based on their loop algebraic presentation.}, number={3}, journal={JOURNAL OF ALGEBRA AND ITS APPLICATIONS}, author={Jing, Naihuan and Xu, Chongbin}, year={2018}, month={Mar} }
 @article{jing_zhang_2018, title={Capelli identity on multiparameter quantum linear groups}, volume={61}, ISSN={["1869-1862"]}, DOI={10.1007/s11425-017-9216-x}, abstractNote={A quantum Capelli identity is given on the multiparameter quantum general linear group based on the (p ij , u)-condition. The multiparameter quantum Pfaffan of the (p ij , u)-quantum group is also introduced and the transformation under the congruent action is given. Generalization to the multiparameter hyper-Pfaffan and relationship with the quantum minors are also investigated.}, number={2}, journal={SCIENCE CHINA-MATHEMATICS}, author={Jing, Naihuan and Zhang, Jian}, year={2018}, month={Feb}, pages={253–268} }
 @article{jing_kozic_molev_yang_2018, title={Center of the quantum affine vertex algebra in type A}, volume={496}, ISSN={["1090-266X"]}, DOI={10.1016/j.jalgebra.2017.10.020}, abstractNote={We consider the quantum vertex algebra associated with the double Yangian in type A as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct algebraically independent families of topological generators of the center at the critical level.}, journal={JOURNAL OF ALGEBRA}, author={Jing, Naihuan and Kozic, Slaven and Molev, Alexander and Yang, Fan}, year={2018}, month={Feb}, pages={138–186} }
 @article{li_jing_tang_2018, title={Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource}, volume={17}, DOI={10.1007/s11128-018-1962-2}, abstractNote={Recently using entanglement as resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has been studied intensively. Zhang. et al. presented protocols to use entanglement to distinguish certain classes of orthogonal product states in $\mathbb{C}^m\otimes \mathbb{C}^n$\cite{Zhang016}. In this paper, we study local distinguishability of multipartite orthogonal product states and provide a practical solution. Our method relies upon a special class of locally indistinguishable multipartite product states introduced by Wang et. al. to build a protocol to distinguishes perfectly multipartitie quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.}, number={8}, journal={Quantum Information Processing}, author={Li, H. Q. and Jing, Naihuan and Tang, X. L.}, year={2018} }
 @article{naihuan_2018, title={From Frobenius character formula to vertex operators}, volume={48}, DOI={10.1360/n012018-00110}, abstractNote={In this paper, simplified derivation of Frobenius character formula for thesymmetric group and Spechts character formula for the wreath products is given. It is shown that vertex operatorshad their presence in Frobenius formula via the multiplication of the Grothendieck ring. The same method is applied tothe Grothendieck ring of the wreath products of symmetric groups and any finite group to givea simplified proof of the Specht formula.}, number={11}, journal={SCIENTIA SINICA Mathematica}, publisher={Science China Press., Co. Ltd.}, author={Naihuan, Jing}, year={2018}, month={Oct}, pages={1717} }
 @article{jing_liu_molev_2018, title={Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D}, volume={361}, ISSN={0010-3616 1432-0916}, url={http://dx.doi.org/10.1007/S00220-018-3185-X}, DOI={10.1007/S00220-018-3185-X}, abstractNote={It is well-known that the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian in type $A$ yields generators of its Drinfeld presentation. Defining relations between these generators are known in an explicit form thus providing an isomorphism between the presentations. It has been an open problem since the pioneering work of Drinfeld to extend this result to the remaining types. We give a solution for the classical types $B$, $C$ and $D$ by constructing an explicit isomorphism between the $R$-matrix and Drinfeld presentations of the Yangian. It is based on an embedding theorem which allows us to consider the Yangian of rank $n-1$ as a subalgebra of the Yangian of rank $n$ of the same type.}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Jing, Naihuan and Liu, Ming and Molev, Alexander}, year={2018}, month={Jun}, pages={827–872} }
 @article{zhao_zhao_jing_2018, title={Multipartite Separability of Density Matrices of Graphs}, volume={57}, ISSN={["1572-9575"]}, url={https://doi.org/10.1007/s10773-018-3829-9}, DOI={10.1007/s10773-018-3829-9}, abstractNote={A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite systems by presenting a class of fully separable states arising from partially symmetric graphs.}, number={10}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, publisher={Springer Nature}, author={Zhao, Hui and Zhao, Jing-Yun and Jing, Naihuan}, year={2018}, month={Oct}, pages={3112–3126} }
 @book{representations of lie algebras, quantum groups and related topics_2018, journal={American Mathematical Society}, year={2018} }
 @article{chen_jing_kong_tan_2018, title={Twisted quantum affinizations and their vertex representations}, volume={59}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.5023790}, DOI={10.1063/1.5023790}, abstractNote={In this paper we generalize Drinfeld's twisted quantum affine algebras to construct twisted quantum algebras for all simply-laced generalized Cartan matrices and present their vertex representation realizations.}, number={8}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Chen, Fulin and Jing, Naihuan and Kong, Fei and Tan, Shaobin}, year={2018}, month={Aug}, pages={081701} }
 @article{adamovic_jing_misra_2017, title={ON PRINCIPAL REALIZATION OF MODULES FOR THE AFFINE LIE ALGEBRA A(1)((1)) AT THE CRITICAL LEVEL}, volume={369}, ISSN={["1088-6850"]}, DOI={10.1090/tran/7009}, abstractNote={We present complete realization of irreducible $A_1 ^{(1)}$-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z-algebra approach to this construction. All irreducible highest weight $A_1 ^{(1)}$-modules at the critical level are realized on the vector space $M_{\tfrac{1}{2} + \Bbb Z} (1) ^{\otimes 2}$ where $M_{\tfrac{1}{2} + \Bbb Z} (1) $ is the polynomial ring ${\Bbb C}[\alpha(-1/2), \alpha(-3/2), ...]$. Explicit combinatorial bases for these modules are also given.}, number={7}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Adamovic, Drazen and Jing, Naihuan and Misra, Kailash C.}, year={2017}, month={Jul}, pages={5113–5136} }
 @article{jing_zhang_2017, title={Quantum hyperdeterminants and hyper-Pfaffians}, volume={287}, ISSN={["1432-1823"]}, DOI={10.1007/s00209-017-1850-y}, abstractNote={The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.}, number={3-4}, journal={MATHEMATISCHE ZEITSCHRIFT}, author={Jing, Naihuan and Zhang, Jian}, year={2017}, month={Dec}, pages={897–914} }
 @article{jing_liu_2017, title={R-matrix realization of two-parameter quantum affine algebra U-r,U-s(<(gl(n))over cap>)}, volume={488}, ISSN={["1090-266X"]}, DOI={10.1016/j.jalgebra.2017.05.028}, abstractNote={We introduce the two-parameter quantum affine algebra U r , s ( gl ˆ n ) via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra.}, journal={JOURNAL OF ALGEBRA}, author={Jing, Naihuan and Liu, Ming}, year={2017}, month={Oct}, pages={1–28} }
 @article{hu_jing_2017, title={Spin characters of hyperoctahedral wreath products}, volume={221}, ISSN={["1873-1376"]}, DOI={10.1016/j.jpaa.2016.12.004}, abstractNote={The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.}, number={9}, journal={JOURNAL OF PURE AND APPLIED ALGEBRA}, author={Hu, Xiaoli and Jing, Naihuan}, year={2017}, month={Sep}, pages={2220–2235} }
 @article{jing_yu_2017, title={Super quantum discord for general two qubit X states}, volume={16}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-017-1547-5}, abstractNote={The exact solutions of the super quantum discord are derived for general two qubit X states in terms of a one-variable function. Several exact solutions of the super quantum discord are given for the general X state over nontrivial regions of a seven-dimensional manifold.}, number={4}, journal={QUANTUM INFORMATION PROCESSING}, author={Jing, Naihuan and Yu, Bing}, year={2017}, month={Apr} }
 @article{xiao_jing_li-jost_2017, title={Uncertainty under quantum measures and quantum memory}, volume={16}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-017-1554-6}, abstractNote={The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements, and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski-Tomamichel-Wehner's bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.}, number={4}, journal={QUANTUM INFORMATION PROCESSING}, publisher={Springer Nature}, author={Xiao, Yunlong and Jing, Naihuan and Li-Jost, Xianqing}, year={2017}, month={Apr} }
 @article{zhang_zhao_jing_fei_2017, title={Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in Multipartite Systems}, volume={56}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-017-3505-5}, abstractNote={We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover, two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased.}, number={11}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Zhang, Ya-Jing and Zhao, Hui and Jing, Naihuan and Fei, Shao-Ming}, year={2017}, month={Nov}, pages={3425–3430} }
 @article{huang_jing_zhang_2016, title={An upper bound of fully entangled fraction of mixed states}, volume={65}, DOI={10.1088/0253-6102/65/6/701}, abstractNote={We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.}, number={6}, journal={Communications in Theoretical Physics}, author={Huang, X. F. and Jing, Naihuan and Zhang, T. G.}, year={2016}, pages={701–704} }
 @article{zhao_guo_jing_fei_2016, title={Construction of bound entangled states based on permutation operators}, volume={15}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-015-1218-3}, abstractNote={We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are PPT (positive partial transpose) and violate the range criterion at the same time. By applying certain operators to given bound entangled states or to one of the subsystems of the given bound entangled states, we obtain a set of new states which are both PPT and violate the range criterion. We show that the derived bound entangled states are not local unitary equivalent to the original bound entangled states by detail examples.}, number={4}, journal={QUANTUM INFORMATION PROCESSING}, author={Zhao, Hui and Guo, Sha and Jing, Naihuan and Fei, Shaoming}, year={2016}, month={Apr}, pages={1529–1538} }
 @article{jing_zhang_2016, title={Drinfeld Realization of Quantum Twisted Affine Algebras via Braid Group}, volume={2016}, ISSN={["1687-9139"]}, DOI={10.1155/2016/4843075}, abstractNote={The Drinfeld realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig’s braid group action.}, journal={ADVANCES IN MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Zhang, Honglian}, year={2016} }
 @article{xiao_jing_li-jost_2016, title={Enhanced Information Exclusion Relations}, volume={6}, ISSN={["2045-2322"]}, DOI={10.1038/srep30440}, abstractNote={In Hall's reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the uncertainty relation, we present new bounds for the information exclusion relation using majorization theory and combinatoric techniques, which reveal further characteristic properties of the overlap matrix between the measurements.}, journal={SCIENTIFIC REPORTS}, author={Xiao, Yunlong and Jing, Naihuan and Li-Jost, Xianqing}, year={2016}, month={Jul} }
 @article{fan_zhou_jing_li_2016, title={Geometric transformations of multidimensional color images based on NASS}, volume={340}, ISSN={["1872-6291"]}, DOI={10.1016/j.ins.2015.12.024}, abstractNote={We present quantum algorithms to realize geometric transformations (two-point swappings, symmetric flips, local flips, orthogonal rotations, and translations) based on an n-qubit normal arbitrary superposition state (NASS). These transformations are implemented using quantum circuits consisting of basic quantum gates, which are constructed with polynomial numbers of single-qubit and two-qubit gates. Complexity analysis shows that the global operators (symmetric flips, local flips, orthogonal rotations) can be implemented with O(n) gates. The proposed geometric transformations are used to facilitate applications of quantum images with low complexity.}, journal={INFORMATION SCIENCES}, author={Fan, Ping and Zhou, Ri-Gui and Jing, Naihuan and Li, Hai-Sheng}, year={2016}, month={May}, pages={191–208} }
 @article{frappat_jing_molev_ragoucy_2016, title={Higher Sugawara Operators for the Quantum Affine Algebras of Type A}, volume={345}, ISSN={["1432-0916"]}, DOI={10.1007/s00220-015-2566-7}, abstractNote={We give explicit formulas for the elements of the center of the completed quantum affine algebra in type $A$ at the critical level which are associated with the fundamental representations. We calculate the images of these elements under a Harish-Chandra-type homomorphism. These images coincide with those in the free field realization of the quantum affine algebra and reproduce generators of the $q$-deformed classical $W$-algebra of Frenkel and Reshetikhin.}, number={2}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Frappat, Luc and Jing, Naihuan and Molev, Alexander and Ragoucy, Eric}, year={2016}, month={Jul}, pages={631–657} }
 @article{xiao_jing_fei_li-jost_2016, title={Improved uncertainty relation in the presence of quantum memory}, volume={49}, ISSN={["1751-8121"]}, DOI={10.1088/1751-8113/49/49/49lt01}, abstractNote={Berta et al’s uncertainty principle in the presence of quantum memory (Berta et al 2010 Nat. Phys. 6 659) reveals uncertainties with quantum side information between the observables. In the recent important work of Coles and Piani (2014 Phys. Rev. A 89 022112), the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation in the presence of quantum memory and find the exact dependence on all d largest overlaps between two measurements on any d-dimensional Hilbert space. Our bound is rigorously shown to be strictly tighter than previous entropic bounds in the presence of quantum memory, which have potential applications to quantum cryptography with entanglement witnesses and quantum key distributions.}, number={49}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Xiao, Yunlong and Jing, Naihuan and Fei, Shao-Ming and Li-Jost, Xianqing}, year={2016}, month={Dec} }
 @article{jing_yang_zhao_2016, title={Local unitary equivalence of quantum states and simultaneous orthogonal equivalence}, volume={57}, ISSN={["1089-7658"]}, DOI={10.1063/1.4954230}, abstractNote={The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂd1 ⊗ ℂd2 are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.}, number={6}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Yang, Min and Zhao, Hui}, year={2016}, month={Jun} }
 @article{jing_wang_2016, title={Modules for double affine Lie algebras}, volume={11}, ISSN={["1673-3576"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84937065004&partnerID=MN8TOARS}, DOI={10.1007/s11464-015-0447-1}, abstractNote={Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.}, number={1}, journal={FRONTIERS OF MATHEMATICS IN CHINA}, author={Jing, Naihuan and Wang, Chunhua}, year={2016}, month={Feb}, pages={89–108} }
 @article{xiao_jing_2016, title={Mutually Exclusive Uncertainty Relations}, volume={6}, ISSN={["2045-2322"]}, DOI={10.1038/srep36616}, abstractNote={The uncertainty principle is one of the characteristic properties of quantum theory based on incompatibility. Apart from the incompatible relation of quantum states, mutually exclusiveness is another remarkable phenomenon in the information- theoretic foundation of quantum theory. We investigate the role of mutual exclusive physical states in the recent work of stronger uncertainty relations for all incompatible observables by Mccone and Pati and generalize the weighted uncertainty relation to the product form as well as their multi-observable analogues. The new bounds capture both incompatibility and mutually exclusiveness, and are tighter compared with the existing bounds.}, journal={SCIENTIFIC REPORTS}, author={Xiao, Yunlong and Jing, Naihuan}, year={2016}, month={Nov} }
 @article{jing_zhang_2016, title={On finite-dimensional representations of two-parameter quantum affine algebras}, volume={15}, ISSN={["1793-6829"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84940849711&partnerID=MN8TOARS}, DOI={10.1142/s0219498816500547}, abstractNote={We introduce the notion of Drinfeld polynomials of two-parameter quantum affine algebras and establish a one-to-one correspondence between finite-dimensional irreducible representations and sets of l-tuples of pairs of polynomials with certain conditions.}, number={3}, journal={JOURNAL OF ALGEBRA AND ITS APPLICATIONS}, author={Jing, Naihuan and Zhang, Honglian}, year={2016}, month={Apr} }
 @article{li_xiao_ma_fei_jing_li-jost_wang_2016, title={Optimal Universal Uncertainty Relations}, volume={6}, ISSN={["2045-2322"]}, DOI={10.1038/srep35735}, abstractNote={We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable recent result of entropic uncertainty relation is the direct-sum majorization relation. In this paper, we illustrate our bounds by showing how they provide a complement to that in [Phys. Rev. A. 89, 052115 (2014)].}, journal={SCIENTIFIC REPORTS}, author={Li, Tao and Xiao, Yunlong and Ma, Teng and Fei, Shao-Ming and Jing, Naihuan and Li-Jost, Xianqing and Wang, Zhi-Xi}, year={2016}, month={Oct} }
 @article{jing_zhang_2016, title={Quantum Permanents and Hafnians via Pfaffians}, volume={106}, ISSN={["1573-0530"]}, DOI={10.1007/s11005-016-0881-3}, abstractNote={Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two-parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian on this special quantum algebra.}, number={10}, journal={LETTERS IN MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Zhang, Jian}, year={2016}, month={Oct}, pages={1451–1464} }
 @article{jing_yu_2016, title={Quantum discord of X-states as optimization of a one variable function}, volume={49}, ISSN={["1751-8121"]}, DOI={10.1088/1751-8113/49/38/385302}, abstractNote={We solve the quantum discord completely as an optimization of a certain one variable function for an arbitrary two qubit X state. Exact solutions of the quantum discord are obtained for several nontrivial regions of the five parametric space for the quantum state. Exceptional solutions are determined via an iterative algorithm.}, number={38}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Jing, Naihuan and Yu, Bing}, year={2016}, month={Sep} }
 @article{gao_liu_bai_jing_2016, title={Rota-Baxter operators on Witt and Virasoro algebras}, volume={108}, ISSN={["1879-1662"]}, url={https://doi.org/10.1016/j.geomphys.2016.06.007}, DOI={10.1016/j.geomphys.2016.06.007}, abstractNote={The homogeneous Rota–Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang–Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.}, journal={JOURNAL OF GEOMETRY AND PHYSICS}, publisher={Elsevier BV}, author={Gao, Xu and Liu, Ming and Bai, Chengming and Jing, Naihuan}, year={2016}, month={Oct}, pages={1–20} }
 @article{xiao_jing_fei_li_li-jost_ma_wang_2016, title={Strong entropic uncertainty relations for multiple measurements}, volume={93}, ISSN={["2469-9934"]}, DOI={10.1103/physreva.93.042125}, abstractNote={In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multimeasurements, with some of them also valid for R\'enyi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an admixture bound for entropic uncertainty relations for multimeasurements. Comparisons among all bounds for multimeasurements are given in two figures.}, number={4}, journal={PHYSICAL REVIEW A}, author={Xiao, Yunlong and Jing, Naihuan and Fei, Shao-Ming and Li, Tao and Li-Jost, Xianqing and Ma, Teng and Wang, Zhi-Xi}, year={2016}, month={Apr} }
 @article{jing_zhang_2016, title={Two-parameter twisted quantum affine algebras}, volume={57}, ISSN={["1089-7658"]}, DOI={10.1063/1.4962722}, abstractNote={We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.}, number={9}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Zhang, Honglian}, year={2016}, month={Sep} }
 @article{xiao_jing_li-jost_fei_2016, title={Uniform Entanglement Frames}, volume={55}, ISSN={["1572-9575"]}, DOI={10.1007/s10773-016-2976-0}, abstractNote={We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of $k$-separable circles via geometric distance for probability vectors, which include at most $(k-1)$-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the $k$-separable states more accurately.}, number={8}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, publisher={Springer Science \mathplus Business Media}, author={Xiao, Yunlong and Jing, Naihuan and Li-Jost, Xianqing and Fei, Shao-Ming}, year={2016}, month={Aug}, pages={3492–3505} }
 @article{jing_rozhkovskaya_2016, title={Vertex Operators Arising from Jacobi-Trudi Identities}, volume={346}, ISSN={["1432-0916"]}, DOI={10.1007/s00220-015-2564-9}, abstractNote={We give an interpretation of the boson-fermion correspondence as a direct consequence of the Jacobi–Trudi identity. This viewpoint enables us to construct from a generalized version of the Jacobi–Trudi identity the action of a Clifford algebra on the polynomial algebras that arrive as analogues of the algebra of symmetric functions. A generalized Giambelli identity is also proved to follow from that identity. As applications, we obtain explicit formulas for vertex operators corresponding to characters of the classical Lie algebras, shifted Schur functions, and generalized Schur symmetric functions associated to linear recurrence relations.}, number={2}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Rozhkovskaya, Natasha}, year={2016}, month={Sep}, pages={679–701} }
 @article{xiao_jing_li-jost_fei_2016, title={Weighted Uncertainty Relations}, volume={6}, ISSN={["2045-2322"]}, DOI={10.1038/srep23201}, abstractNote={Abstract Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations and remove the restriction on the quantum state. Generalization to multi-observable cases is also given and an optimal lower bound for the weighted sum of the variances is obtained in general quantum situation.}, journal={SCIENTIFIC REPORTS}, author={Xiao, Yunlong and Jing, Naihuan and Li-Jost, Xianqing and Fei, Shao-Ming}, year={2016}, month={Mar} }
 @article{jing_li_2015, title={A lift of Schur's Q-functions to the peak algebra}, volume={135}, ISSN={["1096-0899"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84930946254&partnerID=MN8TOARS}, DOI={10.1016/j.jcta.2015.05.006}, abstractNote={We construct a lift of Schur's Q-functions to the peak algebra of the symmetric group, called the noncommutative Schur Q-functions, and extract from them a new natural basis with several nice properties such as the positive right-Pieri rule, combinatorial expansion, etc. Dually, we get a basis of the Stembridge algebra of peak functions refining Schur's P-functions in a simple way.}, journal={JOURNAL OF COMBINATORIAL THEORY SERIES A}, author={Jing, Naihuan and Li, Yunnan}, year={2015}, month={Oct}, pages={268–290} }
 @article{zhao_yu_jing_2015, title={Bound entanglement and distillability of multipartite quantum systems}, volume={13}, ISSN={["1793-6918"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84940732446&partnerID=MN8TOARS}, DOI={10.1142/s0219749915500367}, abstractNote={We construct a class of entangled states in ℋ = ℋA ⊗ ℋB ⊗ ℋC quantum systems with dimℋA = dimℋB = dimℋC = 2 and classify those states with respect to their distillability properties. The states are bound entanglement for the bipartite split (AB) - C. The states are non-positive partial transpose (NPT) entanglement and 1-copy undistillable for the bipartite splits A - (BC) and B - (AC). Moreover, we generalize the results of 2 ⊗ 2 ⊗ 2 systems to the case of 2n ⊗ 2n ⊗ 2n systems.}, number={5}, journal={INTERNATIONAL JOURNAL OF QUANTUM INFORMATION}, author={Zhao, Hui and Yu, Xin-Yu and Jing, Naihuan}, year={2015}, month={Aug} }
 @article{jing_zhang_wang_2015, title={Comment on "One-way deficit of two qubit X states"}, volume={14}, ISSN={["1573-1332"]}, DOI={10.1007/s11128-015-1132-8}, abstractNote={We improve the recent method of Wang et. al to calculate exactly the one-way information deficit of any X-state. Analytical formulas of the one-way information deficit are given for several nontrivial regions of the parameters.}, number={12}, journal={QUANTUM INFORMATION PROCESSING}, author={Jing, Naihuan and Zhang, Xia and Wang, Yao-Kun}, year={2015}, month={Dec}, pages={4511–4521} }
 @article{hu_jing_2015, title={Irreducible projective characters of wreath products}, volume={143}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84919999433&partnerID=MN8TOARS}, DOI={10.1090/s0002-9939-2014-12343-4}, abstractNote={The irreducible character values of the spin wreath products of the symmetric group and an arbitrary finite group are completely determined.}, number={3}, journal={Proceedings of the American Mathematical Society}, author={Hu, X. and Jing, N.}, year={2015}, pages={1015–1026} }
 @article{jing_fei_li_li-jost_zhang_2015, title={Local unitary invariants of generic multiqubit states}, volume={92}, ISSN={["1094-1622"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84939450244&partnerID=MN8TOARS}, DOI={10.1103/physreva.92.022306}, abstractNote={We present a complete set of local unitary invariants for generic multi-qubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in terms of the generalized Bloch representation of the quantum states. In particular, we prove that there are at most 12 polynomial local unitary invariants for two-qubit states and at most 90 polynomials for three-qubit states. Comparison with Makhlin's 18 local unitary invariants is given for two-quibit systems.}, number={2}, journal={PHYSICAL REVIEW A}, author={Jing, Naihuan and Fei, Shao-Ming and Li, Ming and Li-Jost, Xianqing and Zhang, Tinggui}, year={2015}, month={Aug} }
 @article{cai_jing_zhang_2015, title={Modular Macdonald functions and generalized Newton's identity}, volume={442}, ISSN={["1090-266X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84941600026&partnerID=MN8TOARS}, DOI={10.1016/j.jalgebra.2014.10.014}, abstractNote={Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall–Littlewood functions.}, journal={JOURNAL OF ALGEBRA}, author={Cai, Tommy Wuxing and Jing, Naihuan and Zhang, Jian}, year={2015}, month={Nov}, pages={124–136} }
 @article{wang_jing_fei_wang_cao_fan_2015, title={One-way deficit of two-qubit X states}, volume={14}, ISSN={["1573-1332"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84930758767&partnerID=MN8TOARS}, DOI={10.1007/s11128-015-1005-1}, abstractNote={Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath (Oppenheim et al. in Phys Rev Lett 89:180402, 2002). It links quantum correlations with quantum thermodynamics and provides a new standpoint for understanding quantum non-locality. In this paper, we propose a new method to evaluate the one-way deficit for a class of two-qubit states. The dynamic behavior of the one-way deficit under decoherence channel is investigated, and it is shown that the one-way deficit of the $$X$$ states with five parameters is more robust against decoherence than entanglement.}, number={7}, journal={QUANTUM INFORMATION PROCESSING}, author={Wang, Yao-Kun and Jing, Naihuan and Fei, Shao-Ming and Wang, Zhi-Xi and Cao, Jun-Peng and Fan, Heng}, year={2015}, month={Jul}, pages={2487–2497} }
 @book{reversible logic circuits_2015, journal={Nova Science Publishers}, year={2015} }
 @article{jing_li_2015, title={The shifted Poirier-Reutenauer algebra}, volume={281}, ISSN={["1432-1823"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84939240444&partnerID=MN8TOARS}, DOI={10.1007/s00209-015-1496-6}, abstractNote={Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier–Reutenauer algebra is introduced. It is a right coideal subalgebra of the Poirier–Reutenauer algebra, and turns out to be a higher lift of Schur’s P-functions. Its close relations with the peak subalgebra and the Stembridge algebra of peak functions are also uncovered.}, number={3-4}, journal={MATHEMATISCHE ZEITSCHRIFT}, author={Jing, Naihuan and Li, Yunnan}, year={2015}, month={Dec}, pages={611–629} }
 @article{chen_gao_jing_tan_2015, title={Twisted Vertex Operators and Unitary Lie Algebras}, volume={67}, ISSN={["1496-4279"]}, DOI={10.4153/cjm-2014-010-1}, abstractNote={Abstract A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral ${{\mathbb{Z}}_{2}}$ -lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac–Moody Lie algebra of type $A_{n}^{\left( 2 \right)}$ are recovered by the new method.}, number={3}, journal={CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES}, author={Chen, Fulin and Gao, Yun and Jing, Naihuan and Tan, Shaobin}, year={2015}, month={Jun}, pages={573–596} }
 @article{jing_2015, title={Unitary and orthogonal equivalence of sets of matrices}, volume={481}, ISSN={["1873-1856"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84929179522&partnerID=MN8TOARS}, DOI={10.1016/j.laa.2015.04.036}, abstractNote={Two matrices $A$ and $B$ are called unitary (resp. orthogonal) equivalent if $AU=VB$ for two unitary (resp. orthogonal) matrices $U$ and $V$. Using trace identities, criteria are given for simultaneous unitary, orthogonal or complex orthogonal equivalence between two sets of matrices.}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Jing, Naihuan}, year={2015}, month={Sep}, pages={235–242} }
 @article{jing_nie_2015, title={Vertex Operators,Weyl Determinant Formulae and Littlewood Duality}, volume={19}, ISSN={["0219-3094"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84929678323&partnerID=MN8TOARS}, DOI={10.1007/s00026-015-0271-z}, abstractNote={Vertex operator realizations of symplectic and orthogonal Schur functions are studied and expanded. New proofs of determinant identities of irreducible characters for the symplectic and orthogonal groups are given. We also give a new proof of the duality between the universal orthogonal and symplectic Schur functions using vertex operators.}, number={3}, journal={ANNALS OF COMBINATORICS}, author={Jing, Naihuan and Nie, Benzhi}, year={2015}, month={Sep}, pages={427–442} }
 @article{jing_xu_2015, title={Vertex Representations of Toroidal Special Linear Lie Superalgebras}, volume={36}, ISSN={["1860-6261"]}, DOI={10.1007/s11401-015-0921-9}, abstractNote={Based on the loop-algebraic presentation of 2-toroidal Lie superalgebras, free field representation of toroidal Lie superalgebras of type $A(m, n)$ is constructed using both vertex operators and bosonic fields.}, number={3}, journal={CHINESE ANNALS OF MATHEMATICS SERIES B}, author={Jing, Naihuan and Xu, Chongbin}, year={2015}, month={May}, pages={427–436} }
 @article{cai_jing_2014, title={A generalization of Newton's identity and Macdonald functions}, volume={125}, ISSN={["1096-0899"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84906661322&partnerID=MN8TOARS}, DOI={10.1016/j.jcta.2014.04.001}, abstractNote={A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Jack and Macdonald polynomials. We also give a simple proof of the Jing–Józefiak formula for two-row Macdonald functions.}, number={1}, journal={JOURNAL OF COMBINATORIAL THEORY SERIES A}, author={Cai, Tommy Wuxing and Jing, Naihuan}, year={2014}, month={Jul}, pages={342–356} }
 @article{cai_jing_2014, title={Jack vertex operators and realization of Jack functions}, volume={39}, ISSN={["1572-9192"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84891635006&partnerID=MN8TOARS}, DOI={10.1007/s10801-013-0438-9}, abstractNote={We give an iterative method to realize general Jack functions using vertex operators. We first prove some cases of Stanley’s conjecture on positivity of the Littlewood–Richardson coefficients, and then use this method to give a new realization of Jack functions. We also show in general that the images of coefficients of products of Jack vertex operators form a basis of symmetric functions. In particular, this gives a new proof of linear independence for the rectangular and marked rectangular Jack vertex operators. Finally, a generalized Frobenius formula for Jack functions is given and used for evaluation of Dyson integrals and even powers of Vandermonde determinants.}, number={1}, journal={JOURNAL OF ALGEBRAIC COMBINATORICS}, author={Cai, Tommy Wuxing and Jing, Naihuan}, year={2014}, month={Feb}, pages={53–74} }
 @article{jing_xu_2014, title={LIE SUPERALGEBRAS ARISING FROM BOSONIC REPRESENTATION}, volume={42}, ISSN={["1532-4125"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84886393499&partnerID=MN8TOARS}, DOI={10.1080/00927872.2012.713062}, abstractNote={A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains osp(1 | 2n)(1) as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type B(0, n). Furthermore, this algebra is a central extension of the algebra osp(1 | 2n) ⊗ ℂ[s, s −1, t, t −1].}, number={1}, journal={COMMUNICATIONS IN ALGEBRA}, author={Jing, Naihuan and Xu, Chongbin}, year={2014}, month={Jan}, pages={259–270} }
 @article{li_zhang_fei_li-jost_jing_2014, title={Local unitary equivalence of multiqubit mixed quantum states}, volume={89}, ISSN={["1094-1622"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84903512933&partnerID=MN8TOARS}, DOI={10.1103/physreva.89.062325}, abstractNote={We present a computable criterion for completely classifying multiqubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multiqubit systems are locally unitarily equivalent or not. Once a positive answer is obtained, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states.}, number={6}, journal={PHYSICAL REVIEW A}, author={Li, Ming and Zhang, Tinggui and Fei, Shao-Ming and Li-Jost, Xianqing and Jing, Naihuan}, year={2014}, month={Jun} }
 @article{jing_zhang_2014, title={Quantum Pfaffians and hyper-Pfaffians}, volume={265}, ISSN={["1090-2082"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84906491080&partnerID=MN8TOARS}, DOI={10.1016/j.aim.2014.07.007}, abstractNote={The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Pl\"ucker relations for the quantum linear transformations, and then use them to give an optimal set of relations required for the quantum Pfaffian. We then give the formula between the quantum determinant and the quantum Pfaffian and prove that any quantum determinant can be expressed as a quantum Pfaffian. Finally the quantum hyper-Pfaffian is introduced, and we prove a similar result of expressing quantum determinants in terms of quantum hyper-Pfaffians at modular cases.}, journal={ADVANCES IN MATHEMATICS}, author={Jing, Naihuan and Zhang, Jian}, year={2014}, month={Nov}, pages={336–361} }
 @article{jing_liu_2014, title={R-Matrix Realization of Two-Parameter Quantum Group Ur,s(gln)}, volume={2}, ISSN={2194-6701 2194-671X}, url={http://dx.doi.org/10.1007/S40304-014-0037-7}, DOI={10.1007/S40304-014-0037-7}, abstractNote={We provide a Faddeev–Reshetikhin–Takhtajan’s RTT approach to the quantum group $$\mathrm{Fun}(\mathrm{GL}_{r,s}(n))$$ and the quantum enveloping algebra $$U_{r,s}(\mathfrak {gl}_n)$$ corresponding to the two-parameter $$R$$ -matrix. We prove that the quantum determinant $${\det }_{r,s}T$$ is a quasi-central element in $$\mathrm{Fun}(\mathrm{GL}_{r,s}(n))$$ generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang. The explicit formulation provides an interpretation of the deforming parameters, and the quantized algebra $$U_{r,s}(R)$$ is identified to $$U_{r,s}(\mathfrak {gl}_n)$$ as the dual algebra. We then construct $$n-1$$ quasi-central elements in $$U_{r,s}(R)$$ which are analogs of higher Casimir elements in $$U_q(\mathfrak {gl}_n)$$ .}, number={3-4}, journal={Communications in Mathematics and Statistics}, publisher={Springer Science and Business Media LLC}, author={Jing, Naihuan and Liu, Ming}, year={2014}, month={Dec}, pages={211–230} }
 @article{dunbar_jing_misra_2014, title={REALIZATION OF (sl)over-cap(2)(C) AT THE CRITICAL LEVEL}, volume={16}, ISSN={["1793-6683"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84899490482&partnerID=MN8TOARS}, DOI={10.1142/s0219199714500060}, abstractNote={An explicit realization of the affine Lie algebra \hat{sl}_2(C) at the critical level is constructed using a mixture of bosons and parafermions. Subsequently a representation of the associated Lepowsky-Wilson Z-algebra is given on a space of the tensor product of bosonic fields and certain semi-infinite wedge products.}, number={2}, journal={COMMUNICATIONS IN CONTEMPORARY MATHEMATICS}, author={Dunbar, Jonathan and Jing, Naihuan and Misra, Kailash C.}, year={2014}, month={Apr} }
 @article{dong_jing_2014, title={Realizations of Affine Lie Algebra A(1)((1)) at Negative Levels}, volume={85}, ISBN={["978-3-642-55360-8"]}, ISSN={["2194-1009"]}, DOI={10.1007/978-3-642-55361-5_36}, abstractNote={A realization of the affine Lie algebra $${A^{(1)}_1}$$ and the relevant $$Z$$ -algebra at negative level $$-k$$ is given in terms of parafermions. This generalizes the recent work on realization of the affine Lie algebra at the critical level.}, journal={ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS (AGMP)}, author={Dong, Jilan and Jing, Naihuan}, year={2014}, pages={603–616} }
 @article{jing_li_li-jost_zhang_fei_2014, title={SLOCC invariants for multipartite mixed states}, volume={47}, ISSN={["1751-8121"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84929171716&partnerID=MN8TOARS}, DOI={10.1088/1751-8113/47/21/215303}, abstractNote={We construct a nontrivial set of invariants for any multipartite mixed states under the stochastic local operations and classical communication symmetry. These invariants are given by hyperdeterminants and independent of basis change. In particular, a family of d2 invariants for arbitrary d-dimensional even partite mixed states are explicitly given.}, number={21}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Jing, Naihuan and Li, Ming and Li-Jost, Xianqing and Zhang, Tinggui and Fei, Shao-Ming}, year={2014}, month={May} }
 @article{hu_jing_2014, title={Spin characters of generalized symmetric groups}, volume={173}, ISSN={["1436-5081"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84896394195&partnerID=MN8TOARS}, DOI={10.1007/s00605-013-0525-y}, abstractNote={In 1911 Schur computed the spin character values of the symmetric group using two important ingredients: the first one later became famously known as the Schur Q-functions and the second one was certain creative construction of the projective characters on Clifford algebras. In the context of the McKay correspondence and affine Lie algebras, the first part was generalized to all wreath products by the vertex operator calculus in Frenkel et al. (Duke Math J 111:51–96, 2002) where a large part of the character table was produced. The current paper generalizes the second part and provides the missing projective character values for the wreath product of the symmetric group with a finite abelian group. Our approach relies on Mackey–Wigner’s little groups to construct irreducible modules. In particular, projective modules and spin character values of all classical Weyl groups are obtained.}, number={4}, journal={MONATSHEFTE FUR MATHEMATIK}, author={Hu, Xiaoli and Jing, Naihuan}, year={2014}, month={Apr}, pages={495–518} }
 @article{jing_liu_2014, title={Twisted Quantum Toroidal Algebras T-q(-)(g)}, volume={104}, ISSN={["1573-0530"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84904135738&partnerID=MN8TOARS}, DOI={10.1007/s11005-014-0711-4}, abstractNote={We construct a principally graded quantum loop algebra for the Kac–Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.}, number={9}, journal={LETTERS IN MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Liu, Rongjia}, year={2014}, month={Sep}, pages={1137–1145} }
 @article{zhang_jing_li-jost_zhao_fei_2013, title={A note on state decomposition independent local invariants}, volume={67}, ISSN={["1434-6079"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84887595495&partnerID=MN8TOARS}, DOI={10.1140/epjd/e2013-40068-7}, abstractNote={We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations.}, number={8}, journal={EUROPEAN PHYSICAL JOURNAL D}, author={Zhang, Ting-Gui and Jing, Naihuan and Li-Jost, Xianqing and Zhao, Ming-Jing and Fei, Shao-Ming}, year={2013}, month={Aug} }
 @article{jing_liu_2013, title={A twisted quantum toroidal algebra}, volume={8}, ISSN={["1673-3576"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84882836530&partnerID=MN8TOARS}, DOI={10.1007/s11464-013-0316-8}, abstractNote={As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A_1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space.}, number={5}, journal={FRONTIERS OF MATHEMATICS IN CHINA}, author={Jing, Naihuan and Liu, Rongjia}, year={2013}, month={Oct}, pages={1117–1128} }
 @article{liu_bai_ge_jing_2013, title={Generalized Bell states and principal realization of the Yangian Y(sl(N))}, volume={54}, ISSN={["1089-7658"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84874725231&partnerID=MN8TOARS}, DOI={10.1063/1.4789317}, abstractNote={We prove that the action of the Yangian algebra Y(slN) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number J2 is also explicitly computed, which gives an explanation for these maximally entangled states.}, number={2}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={Liu, Ming and Bai, Chengming and Ge, Mo-Lin and Jing, Naihuan}, year={2013}, month={Feb} }
 @article{hu_jing_cai_2013, title={Generalized McKay quivers of rank three}, volume={29}, ISSN={["1439-7617"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84879197022&partnerID=MN8TOARS}, DOI={10.1007/s10114-013-1005-y}, abstractNote={For each finite subgroup G of SL n (ℂ), we introduce the generalized Cartan matrix A G in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semidefiniteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL 3(ℂ) are explicitly described and classified based on representation theory.}, number={7}, journal={ACTA MATHEMATICA SINICA-ENGLISH SERIES}, author={Hu, Xiao Li and Jing, Naihuan and Cai, Wu Xing}, year={2013}, month={Jul}, pages={1351–1368} }
 @article{jing_liu_2013, title={Isomorphism between two realizations of the Yangian Y(so(3))}, volume={46}, ISSN={["1751-8121"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84873890099&partnerID=MN8TOARS}, DOI={10.1088/1751-8113/46/7/075201}, abstractNote={The isomorphism between Drinfeld’s new realization and the FRT realization is proved for the Yangian algebra Y(so3)?> using Gauss decomposition.}, number={7}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Jing, Naihuan and Liu, Ming}, year={2013}, month={Feb} }
 @article{zhang_huang_li-jost_jing_fei_2013, title={Separable State Decompositions for a Class of Mixed States}, volume={52}, ISSN={["1572-9575"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84884908137&partnerID=MN8TOARS}, DOI={10.1007/s10773-013-1727-8}, abstractNote={We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n×n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT.}, number={11}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Zhang, Ting-Gui and Huang, Xiaofen and Li-Jost, Xianqing and Jing, Naihuan and Fei, Shao-Ming}, year={2013}, month={Nov}, pages={4148–4154} }
 @article{cai_jing_2012, title={Applications of a Laplace–Beltrami operator for Jack polynomials}, volume={33}, ISSN={0195-6698}, url={http://dx.doi.org/10.1016/j.ejc.2011.11.003}, DOI={10.1016/j.ejc.2011.11.003}, abstractNote={We use a new method to study the Laplace-Beltrami type operator on the Fock space of symmetric functions, and as an example of our explicit computation we show that the Jack symmetric functions are the only family of eigenvectors of the differential operator. As applications of this explicit method we find a combinatorial formula for Jack symmetric functions and the Littlewood-Richardson coefficients in the Jack case. As further applications, we obtain a new determinantal formula for Jack symmetric functions. We also obtained a generalized raising operator formula for Jack symmetric functions, and a formula for the explicit action of Virasoro operators. Special cases of our formulas imply Mimachi-Yamada's result on Jack symmetric functions of rectangular shapes, as well as the explicit formula for Jack functions of two rows or two columns.}, number={4}, journal={European Journal of Combinatorics}, publisher={Elsevier BV}, author={Cai, Wuxing and Jing, Naihuan}, year={2012}, month={May}, pages={556–571} }
 @article{hird_jing_stitzinger_2012, title={CODES AND SHIFTED CODES}, volume={22}, ISSN={["1793-6500"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84865779191&partnerID=MN8TOARS}, DOI={10.1142/s0218196712500543}, abstractNote={The action of the Bernstein operators on Schur functions was given in terms of codes by Carrell and Goulden (2011) and extended to the analog in Schur Q-functions in our previous work. We define a new combinatorial model of extended codes and show that both of these results follow from a natural combinatorial relation induced on codes. The new algebraic structure provides a natural setting for Schur functions indexed by compositions.}, number={6}, journal={INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION}, author={Hird, J. T. and Jing, Naihuan and Stitzinger, Ernest}, year={2012}, month={Sep} }
 @article{wang_jing_li_2012, title={Lie triple derivation algebra of Virasoro-like algebra}, volume={38}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84865502717&partnerID=MN8TOARS}, number={1}, journal={Bulletin of the Iranian Mathematical Society}, author={Wang, H.-T. and Jing, N. and Li, Q.-G.}, year={2012}, pages={17–26} }
 @article{zhou_zhang_fei_jing_li-jost_2012, title={Local unitary equivalence of arbitrary dimensional bipartite quantum states}, volume={86}, ISSN={["1094-1622"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84863713546&partnerID=MN8TOARS}, DOI={10.1103/physreva.86.010303}, abstractNote={The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary conditions for the equivalence of quantum states under local unitary transformations: two density matrices are locally equivalent if and only if all these invariants have equal values.}, number={1}, journal={PHYSICAL REVIEW A}, author={Zhou, Chunqin and Zhang, Ting-Gui and Fei, Shao-Ming and Jing, Naihuan and Li-Jost, Xianqing}, year={2012}, month={Jul} }
 @article{jing_2012, title={On Classes of Local Unitary Transformations}, volume={19}, ISSN={["1005-3867"]}, DOI={10.1142/s1005386712000181}, abstractNote={We give a one-to-one correspondence between classes of density matrices under local unitary invariance and the double cosets of unitary groups. We show that the interrelationship among classes of local unitary equivalent multi-partite mixed states is independent from the actual values of the eigenvalues and only depends on the multiplicities of the eigenvalues. The interpretation in terms of homogeneous spaces of unitary groups is also discussed.}, number={2}, journal={ALGEBRA COLLOQUIUM}, author={Jing, Naihuan}, year={2012}, month={Jun}, pages={283–292} }
 @article{jing_2012, title={On classes of local unitary transformations}, volume={19}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84859558364&partnerID=MN8TOARS}, number={2}, journal={Algebra Colloquium}, author={Jing, N.}, year={2012}, pages={283–292} }
 @article{zhang_jing_2012, title={Preface}, volume={19}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84859529475&partnerID=MN8TOARS}, number={2}, journal={Algebra Colloquium}, author={Zhang, J. and Jing, N.}, year={2012} }
 @article{jing_liu_2012, title={Principal Realization of Twisted Yangian}, volume={102}, ISSN={["1573-0530"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84865826850&partnerID=MN8TOARS}, DOI={10.1007/s11005-012-0559-4}, abstractNote={We give the principal realization of the twisted Yangians of orthogonal and symplectic types. The new bases are interpreted in terms of discrete Fourier transform over the cyclic group $${\mathbb Z_N}$$ .}, number={1}, journal={LETTERS IN MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Liu, Ming}, year={2012}, month={Oct}, pages={91–105} }
 @book{quantized algebra and physics_2012, journal={World Scientific Publishing Co. Pte. Ltd}, year={2012} }
 @article{gao_jing_2011, title={A Quantized Tits-Kantor-Koecher Algebra}, volume={14}, ISSN={["1386-923X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-80052871486&partnerID=MN8TOARS}, DOI={10.1007/s10468-009-9205-y}, abstractNote={We propose a quantum analogue of a Tits-Kantor-Koecher algebra with a Jordan torus as an coordinated algebra by looking at the vertex operator construction over a Fock space.}, number={3}, journal={ALGEBRAS AND REPRESENTATION THEORY}, author={Gao, Yun and Jing, Naihuan}, year={2011}, month={Jun}, pages={589–599} }
 @article{hird_jing_stitzinger_2011, title={CODES AND SHIFTED CODES OF PARTITIONS}, volume={21}, ISSN={["1793-6500"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84555186874&partnerID=MN8TOARS}, DOI={10.1142/s0218196711006595}, abstractNote={In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's theorem. We show that this identity is a straightforward consequence of the classical result. We also show how a similar approach using the codes of partitions can be generalized from Schur functions to also include Schur Q-functions and derive the combinatorial formulation for both cases. We then apply them by examining the Littlewood–Richardson and Pieri rules.}, number={8}, journal={INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION}, author={Hird, J. T. and Jing, Naihuan and Stitzinger, Ernest}, year={2011}, month={Dec}, pages={1447–1462} }
 @article{jing_zhang_2011, title={TWO-PARAMETER QUANTUM VERTEX REPRESENTATIONS VIA FINITE GROUPS AND THE MCKAY CORRESPONDENCE}, volume={363}, ISSN={["1088-6850"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79953004511&partnerID=MN8TOARS}, DOI={10.1090/s0002-9947-2011-05284-0}, abstractNote={We provide a group-theoretic realization of two-parameter quantum toroidal algebras using finite subgroups of $SL_2(\mathbb C)$ via McKay correspondence. In particular our construction contains the vertex representation of the two-parameter quantum affine algebras of $ADE$ types as special subalgebras.}, number={7}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Jing, Naihuan and Zhang, Honglian}, year={2011}, month={Jul}, pages={3769–3797} }
 @article{gao_jing_2010, title={A Quantized Tits-Kantor-Koecher Algebra}, volume={13}, ISSN={["1386-923X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-77952096651&partnerID=MN8TOARS}, DOI={10.1007/s10468-008-9115-4}, abstractNote={We propose a quantum analogue of a Tits–Kantor–Koecher algebra with a Jordan torus as an coordinated algebra by looking at the vertex operator construction over a Fock space.}, number={2}, journal={ALGEBRAS AND REPRESENTATION THEORY}, author={Gao, Yun and Jing, Naihuan}, year={2010}, month={Apr}, pages={207–217} }
 @article{jing_zhang_2010, title={ADDENDUM TO "DRINFELD REALIZATION OF TWISTED QUANTUM AFFINE ALGEBRAS"}, volume={38}, ISSN={["1532-4125"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-77957732758&partnerID=MN8TOARS}, DOI={10.1080/00927870902933213}, abstractNote={We provide necessary details to several arguments that appeared in our previous paper “Drinfeld Realization of Twisted Quantum Affine Algebras,” Commun. Algebra 35 (2007) 3683–3698.}, number={9}, journal={COMMUNICATIONS IN ALGEBRA}, author={Jing, Naihuan and Zhang, Honglian}, year={2010}, pages={3484–3488} }
 @article{jing_misra_2010, title={Fermionic realization of toroidal Lie algebras of classical types}, volume={324}, ISSN={["1090-266X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-77952959663&partnerID=MN8TOARS}, DOI={10.1016/j.jalgebra.2010.03.021}, abstractNote={We use fermionic operators to construct toroidal Lie algebras of classical types, including in particular that of symplectic affine algebras, which is first realized by fermions.}, number={2}, journal={JOURNAL OF ALGEBRA}, author={Jing, Naihuan and Misra, Kailash C.}, year={2010}, month={Jul}, pages={183–194} }
 @article{cai_jing_2010, title={On vertex operator realizations of Jack functions}, volume={32}, ISSN={["0925-9899"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78049527579&partnerID=MN8TOARS}, DOI={10.1007/s10801-010-0228-6}, abstractNote={On the vertex operator algebra associated with a rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of rectangular shapes as well as marked rectangular shapes.}, number={4}, journal={JOURNAL OF ALGEBRAIC COMBINATORICS}, author={Cai, Wuxing and Jing, Naihuan}, year={2010}, month={Dec}, pages={579–595} }
 @book{quantum affine algebras, extended affine lie algebras, and their applications_2010, journal={American Mathematical Society}, year={2010} }
 @article{fei_albeverio_cabello_jing_goswami_2010, title={Quantum information and entanglement}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84890161694&partnerID=MN8TOARS}, DOI={10.1155/2010/657878}, abstractNote={1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China 2 Institute of Applied Mathematics, University of Bonn, 53115 Bonn, Germany 3 Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain 4 Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA 5 Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India}, journal={Advances in Mathematical Physics}, author={Fei, S.-M. and Albeverio, S. and Cabello, A. and Jing, N. and Goswami, D.}, year={2010} }
 @article{jing_misra_xu_2009, title={BOSONIC REALIZATION OF TOROIDAL LIE ALGEBRAS OF CLASSICAL TYPES}, volume={137}, ISSN={["1088-6826"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-77950857029&partnerID=MN8TOARS}, DOI={10.1090/S0002-9939-09-09942-0}, abstractNote={We use fermionic operators to construct toroidal Lie algebras of classical types, including in particular that of symplectic affine algebras, which is first realized by fermions.}, number={11}, journal={PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Jing, Naihuan and Misra, Kailash C. and Xu, Chongbin}, year={2009}, month={Nov}, pages={3609–3618} }
 @article{jing_zhang_2009, title={Fermionic Realization of Two-Parameter Quantum Affine Algebra Ur,s((sln) over cap)}, volume={89}, ISSN={["0377-9017"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-70349220866&partnerID=MN8TOARS}, DOI={10.1007/s11005-009-0329-0}, abstractNote={We construct all fundamental modules for the two parameter quantum affine algebra of type A using a combinatorial model of Young diagrams. In particular, we also give a fermionic realization of the two-parameter quantum affine algebra.}, number={2}, journal={LETTERS IN MATHEMATICAL PHYSICS}, author={Jing, Naihuan and Zhang, Honglian}, year={2009}, month={Aug}, pages={159–170} }
 @article{bai_ge_jing_2009, title={Principal realization of the Yangian Y(gl,(n))}, volume={50}, ISSN={["1089-7658"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-59349083349&partnerID=MN8TOARS}, DOI={10.1063/1.3050319}, abstractNote={Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian Y(sl(n)) using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan–Weyl basis is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.}, number={1}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={Bai, Cheng-Ming and Ge, Mo-Lin and Jing, Naihuan}, year={2009}, month={Jan} }
 @article{zhang_jing_ge_2008, title={Quantum algebras associated with Bell states}, volume={41}, ISSN={["1751-8121"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-43049099685&partnerID=MN8TOARS}, DOI={10.1088/1751-8113/41/5/055310}, abstractNote={The Bell matrix has become an interesting interdisciplinary topic involving quantum information theory and the Yang–Baxter equation. It is an antisymmetric unitary solution of the braided Yang–Baxter equation and yields all the Bell states by acting on the product basis. In this paper, using the Faddeev–Reshetikhin–Takhtadjian (FRT) construction, we obtain a quantum algebra associated with the Bell matrix. We explore two characteristic algebraic structures in its four-dimensional representation. One is a representation with a composition series, namely, it has irreducible subrepresentations but is not completely reducible. The other is a direct sum of two-dimensional cyclic representations, and can be spanned by four maximally entangled states as local unitary transformations of the Bell states. Both of them are expected to be realized in physical systems and exploited in quantum information theory. Besides, we present the other quantum algebra associated with the unitary evolution of the Bell states (or the Yang–Baxterization of the Bell matrix).}, number={5}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Zhang, Yong and Jing, Naihuan and Ge, Mo-Lin}, year={2008}, month={Feb} }
 @article{huang_jing_2008, title={Separability of multi-partite quantum states}, volume={41}, ISSN={["1751-8121"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-54749142880&partnerID=MN8TOARS}, DOI={10.1088/1751-8113/41/39/395302}, abstractNote={We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in terms of the spectrum of the factor operators in the tensor summands.}, number={39}, journal={JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, author={Huang, Xiaofen and Jing, Naihuan}, year={2008}, month={Oct} }
 @article{jing_xia_2007, title={Affine Lie algebras and product-sum identities}, volume={314}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34250027840&partnerID=MN8TOARS}, DOI={10.1016/j.jalgebra.2007.04.004}, abstractNote={We provide four different decompositions for a special infinite product first studied by I. Schur. Our product–sum decomposition gives two more correspondences between subsets of partitions with parts congruent to 1 or 5 modulo 6. Our method uses a special vertex representation of affine Lie algebra C 3 ( 1 ) and admissible representations of A 1 ( 1 ) as well as quintuple product identity.}, number={2}, journal={JOURNAL OF ALGEBRA}, author={Jing, Naihuan and Xia, Li-meng}, year={2007}, month={Aug}, pages={538–552} }
 @article{zhang_jing_2007, title={Drinfeld realization of twisted quantum affine algebras}, volume={35}, ISSN={["0092-7872"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-35449000413&partnerID=MN8TOARS}, DOI={10.1080/00927870701404713}, abstractNote={The quantum affine algebra has two realizations, the usual Drinfeld–Jimbo definition and a new Drinfeld realization given by Drinfeld. In this article, we use the adjoint action to prove that these two realizations are isomorphic for the twisted quantum affine algebra.}, number={11}, journal={COMMUNICATIONS IN ALGEBRA}, author={Zhang, Honglian and Jing, Naihuan}, year={2007}, pages={3683–3698} }
 @article{fei_jing_sun_2006, title={Hermitian tensor product approximation of complex matrices and separability}, volume={57}, ISSN={["0034-4877"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33745738544&partnerID=MN8TOARS}, DOI={10.1016/S0034-4877(06)80021-2}, abstractNote={The approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space $H_1\otimes H_2$ in terms of the sum of tensor products of Hermitian matrices on $H_1$ and $H_2$ is presented. From this construction the separability of quantum states is discussed.}, number={2}, journal={REPORTS ON MATHEMATICAL PHYSICS}, author={Fei, SM and Jing, NH and Sun, BZ}, year={2006}, month={Apr}, pages={271–288} }
 @article{jing_misra_tan_2005, title={Bosonic realizations of higher-level toroidal Lie algebras}, volume={219}, ISSN={["0030-8730"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-30544448525&partnerID=MN8TOARS}, DOI={10.2140/pjm.2005.219.285}, abstractNote={We construct realizations for the 2-toroidal Lie algebra associated with the Lie algebra A1 using vertex operators based on bosonic elds. In particular our construction realizes higher-level representations of the 2-toroidal algebra for any given pair of levels (k0;k1) with k00. We also construct a smaller module of level (k0;0) for the toroidal algebra from the Fock space using certain screening vertex operator, and this later representation generalizes the higher-level construction of the ane Lie algebra 2.}, number={2}, journal={PACIFIC JOURNAL OF MATHEMATICS}, author={Jing, NH and Misra, K and Tan, SB}, year={2005}, month={Apr}, pages={285–301} }
 @article{fei_jing_2005, title={Equivalence of quantum states under local unitary transformations}, volume={342}, ISSN={["1873-2429"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-20444462791&partnerID=MN8TOARS}, DOI={10.1016/j.physleta.2005.05.050}, abstractNote={In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented.}, number={1-2}, journal={PHYSICS LETTERS A}, author={Fei, SM and Jing, NH}, year={2005}, month={Jul}, pages={77–81} }
 @article{gao_jing_2004, title={U-q (gl(N)) action on gl(N)-modules and quantum toroidal algebras}, volume={273}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-1342268342&partnerID=MN8TOARS}, DOI={10.1016/j.jalgebra.2003.09.046}, abstractNote={We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic representation of the affine Lie algebra $gl_n$ and show that the simple generators give rise a realization of the quantum toroidal algebra with two parameters.}, number={1}, journal={JOURNAL OF ALGEBRA}, author={Gao, Y and Jing, NH}, year={2004}, month={Mar}, pages={320–343} }
 @article{jing_2004, title={Vertex Representations and McKay Correspondence}, volume={11}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-1842528779&partnerID=MN8TOARS}, number={1}, journal={Algebra Colloquium}, author={Jing, N.}, year={2004}, pages={53–70} }
 @book{algebraic combinatorics and quantum groups_2003, journal={World Scientific Publishing Co., Inc}, year={2003} }
 @article{jing_wang_2002, title={Twisted vertex representations and spin characters}, volume={239}, ISSN={["0025-5874"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0036012928&partnerID=MN8TOARS}, DOI={10.1007/s002090100340}, abstractNote={We establish a new group-theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras of ADE types in the same spirit of our new approach to the McKay correspondence. Our vertex operator construction provides a unified description to the character tables for the spin cover of the wreath product of the twisted hyperoctahedral groups and an arbitrary finite group.}, number={4}, journal={MATHEMATISCHE ZEITSCHRIFT}, author={Jing, NH and Wang, WQ}, year={2002}, month={Apr}, pages={715–746} }
 @article{frenkel_jing_wang_2002, title={Twisted vertex representations via spin groups and the McKay correspondence}, volume={111}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0037082243&partnerID=MN8TOARS}, DOI={10.1215/dmj/1008706939}, abstractNote={We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group $\Gamma$ and a virtual character of $\Gamma$, we construct twisted vertex operators on the Fock space spanned by the super spin characters of the spin wreath products $\Gamma\wr \tilde {S}_n$ of $\Gamma$ and a double cover of the symmetric group $S_n$ for all $n$. When $\Gamma$ is a subgroup of ${\rm SL}_2(\mathbb {C})$ with the McKay virtual character, our construction gives a group-theoretic realization of the basic representations of the twisted affine and twisted toroidal Lie algebras. When $\Gamma$ is an arbitrary finite group and the virtual character is trivial, our vertex operator construction yields the spin character tables for $\Gamma\wr \tilde {S}_n$.}, number={1}, journal={Duke Mathematical Journal}, author={Frenkel, I.B. and Jing, N. and Wang, W.}, year={2002}, pages={51–96} }
 @article{hara_jing_misra_2001, title={BRST resolution for the principally graded Wakimoto module of (sl)over-cap(2)}, volume={58}, ISSN={["0377-9017"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0041814659&partnerID=MN8TOARS}, DOI={10.1023/A:1014559525117}, number={3}, journal={LETTERS IN MATHEMATICAL PHYSICS}, author={Hara, Y and Jing, NH and Misra, K}, year={2001}, month={Dec}, pages={181–188} }
 @article{jing_misra_savage_2001, title={On multi-color partitions and the generalized Rogers-Ramanujan identities}, volume={3}, ISSN={["0219-1997"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-27144449078&partnerID=MN8TOARS}, DOI={10.1142/S0219199701000482}, abstractNote={ Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers–Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical physics. One of these areas is representation theory of infinite dimensional Lie algebras, where various known interpretations of these identities have led to interesting applications. Motivated by their connections with Lie algebra representation theory, we give a new interpretation of a sum related to generalized Rogers–Ramanujan identities in terms of multi-color partitions. }, number={4}, journal={COMMUNICATIONS IN CONTEMPORARY MATHEMATICS}, author={Jing, NH and Misra, KC and Savage, CD}, year={2001}, month={Nov}, pages={533–548} }
 @article{chari_jing_2001, title={Realization of level one representations of $U\sb q(\hat{\mathfrak {g}})$ at a root of unity}, volume={108}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0013121572&partnerID=MN8TOARS}, DOI={10.1215/s0012-7094-01-10816-8}, abstractNote={Using vertex operators, we construct explicitly Lusztig's $\mathbb Z[q, q^{-1}]$-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We then realize the level one irreducible modules at roots of unity and show that the q-dimension is still given by the Weyl-Kac character formula. As a consequence we also answer the corresponding question of realizing the affine Kac-Moody Lie algebras of simply laced type at level one in finite characteristic.}, number={1}, journal={Duke Mathematical Journal}, author={Chari, V. and Jing, Naihuan}, year={2001}, pages={183–197} }
 @article{ismail_jing_2001, title={q-discriminants and vertex operators}, volume={27}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0035413459&partnerID=MN8TOARS}, DOI={10.1006/aama.2001.0745}, abstractNote={Discriminants and their discrete and q-analogs are usually studied in the q-analysis theory. In this paper we propose a unified realization of discriminants using vertex operators coming from infinite dimensional Lie algebras and their quantum deformations as well as Yangian deformations. In this picture all of them appear as matrix coefficients of certain products of vertex operators according to respective cases.}, number={2-3}, journal={Advances in Applied Mathematics}, author={Ismail, M.E.H. and Jing, N.}, year={2001}, pages={482–492} }
 @article{ding_jing_2000, title={On a Combinatorial Identity}, volume={2000}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0346737810&partnerID=MN8TOARS}, number={6}, journal={International Mathematics Research Notices}, author={Ding, J. and Jing, N.}, year={2000}, pages={324–332} }
 @article{jing_2000, title={Quantum Z-algebras and representations of quantum affine algebras}, volume={28}, ISSN={["1532-4125"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-26044457008&partnerID=MN8TOARS}, DOI={10.1080/00927870008826863}, abstractNote={Generalizing our earlier work, we introduce the homogeneous quantum Z-algebras for all quantum affine algebras U q(gcirc;) of type one. With the new algebras we unite previously scattered realizations of quantum affine algebras in various cases. As a result we find a realization of .}, number={2}, journal={COMMUNICATIONS IN ALGEBRA}, author={Jing, NH}, year={2000}, pages={829–844} }
 @article{frenkel_jing_wang_2000, title={Quantum vertex representations via finite groups and the McKay correspondence}, volume={211}, ISSN={["0010-3616"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0347016085&partnerID=MN8TOARS}, DOI={10.1007/s002200050817}, abstractNote={We establish a q-analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ we construct a Fock space and associated vertex operators in terms of wreath products of $Γ×ℂ× and the symmetric groups. An important special case is obtained when Γ is a finite subgroup of SU 2, where our construction yields a group theoretic realization of the representations of the quantum affine and quantum toroidal algebras of ADE type.}, number={2}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Frenkel, IB and Jing, NH and Wang, WQ}, year={2000}, month={Apr}, pages={365–393} }
 @article{jing_2000, title={The order of groups satisfying a converse to Lagrange's theorem}, volume={47}, ISSN={["0025-5793"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0039013810&partnerID=MN8TOARS}, DOI={10.1112/S0025579300015813}, abstractNote={One of the converse statements to Lagrange's theorem is that, for each subgroup H of G and any prime factor p of |G: H|, there exists a subgroup K such that H ≤ K ≤ G with |K: H| = p. This paper treats integers n such that all groups of order n have this property.}, number={93-94}, journal={MATHEMATIKA}, author={Jing, NH}, year={2000}, pages={197–204} }
 @article{frenkel_jing_wang_2000, title={Vertex representations via finite groups and the McKay correspondence}, volume={2000}, ISSN={["1687-0247"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0347016085&partnerID=MN8TOARS}, DOI={10.1155/s107379280000012x}, abstractNote={Abstract:We establish a q-analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ we construct a Fock space and associated vertex operators in terms of wreath products of $Γ×ℂ× and the symmetric groups. An important special case is obtained when Γ is a finite subgroup of SU2, where our construction yields a group theoretic realization of the representations of the quantum affine and quantum toroidal algebras of ADE type.}, number={4}, journal={INTERNATIONAL MATHEMATICS RESEARCH NOTICES}, author={Frenkel, IB and Jing, NH and Wang, WQ}, year={2000}, pages={195–222} }
 @article{jing_misra_okado_2000, title={q-wedge modules for quantized enveloping algebras of classical type}, volume={230}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0034662533&partnerID=MN8TOARS}, DOI={10.1006/jabr.2000.8325}, abstractNote={Abstract We use the fusion construction in twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a by-product we uniformly realize all non-spin fundamental modules for quantized enveloping algebras of classical types, and show that they admit natural crystal bases as modules for the (derived) twisted quantum affine algebra. These crystal bases are parametrized in terms of the q -wedge products.}, number={2}, journal={JOURNAL OF ALGEBRA}, author={Jing, NH and Misra, KC and Okado, M}, year={2000}, month={Aug}, pages={518–539} }
 @article{jing_zhang_1999, title={Gorensteinness of invariant subrings of quantum algebras}, volume={221}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0033570733&partnerID=MN8TOARS}, DOI={10.1006/jabr.1999.8023}, abstractNote={Abstract We prove Auslander–Gorenstein and GKdim–Macaulay properties for certain invariant subrings of some quantum algebras, the Weyl algebras, and the universal enveloping algebras of finite-dimensional Lie algebras.}, number={2}, journal={JOURNAL OF ALGEBRA}, author={Jing, N and Zhang, JJ}, year={1999}, month={Nov}, pages={669–691} }
 @article{jing_1999, title={Level one representations of U-q(G(2)((1)))}, volume={127}, ISSN={["0002-9939"]}, DOI={10.1090/S0002-9939-99-04740-1}, abstractNote={We construct level one representations of the quantum affine algebra $U_q(G_2^{(1)})$ by vertex operators from bosonic fields.}, number={1}, journal={PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Jing, NH}, year={1999}, month={Jan}, pages={21–27} }
 @article{jing_1999, title={Level one representations of Uq(G2 (1))}, volume={127}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-22444452806&partnerID=MN8TOARS}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Jing, N.}, year={1999}, pages={21–27} }
 @article{jing_koyama_misra_1999, title={Level one representations of quantum affine algebras Uq(C n (1))}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-53149123269&partnerID=MN8TOARS}, number={2}, journal={Selecta Mathematica, New Series}, author={Jing, N. and Koyama, Y. and Misra, K.C.}, year={1999}, pages={243–255} }
 @article{jing_lyerly_1999, title={Level two vertex representations of G(1) 2}, volume={27}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0033243918&partnerID=MN8TOARS}, number={9}, journal={Communications in Algebra}, author={Jing, N. and Lyerly, C.M.}, year={1999}, pages={4355–4362} }
 @article{jing_lyerly_1999, title={Level two vertex representations of G(2)((1))}, volume={27}, ISSN={["0092-7872"]}, DOI={10.1080/00927879908826702}, abstractNote={We construct explicitly a level two representation of the affine Lie algebra using interactive bosonic fields.}, number={9}, journal={COMMUNICATIONS IN ALGEBRA}, author={Jing, NH and Lyerly, CM}, year={1999}, pages={4355–4362} }
 @book{jing_misra_1999, title={Recent developments in quantum affine algebras and related topics: Representations of affine and quantum affine algebras and their applications, North Carolina State University, May 21-24, 1998 / Naihuan Jing, Kailash C. Misra, editors}, ISBN={0821811991}, DOI={10.1090/conm/248}, abstractNote={The polynomial behavior of weight multiplicities for classical simple Lie algebras and classical affine Kac-Moody algebras by G. Benkart, S.-J. Kang, H. Lee, and D.-U. Shin A note on embeddings of some Lie algebras defined by matrices by S. Berman and S. Tan Principal realization for the extended affine Lie algebra of type $sl_2$ with coordinates in a simple quantum torus with two generators by S. Berman and J. Szmigielski Monomial bases of quantized enveloping algebras by V. Chari and N. Xi Quantized W-algebra of ${\mathfrak sl}(2,1)$: a construction from the quantization of screening operators by J. Ding and B. Feigin Affine algebras and non-perturbative symmetries in superstring theory by L. Dolan Automorphism groups and twisted modules for lattice vertex operator algebras by C. Dong and K. Nagatomo Truncated meanders by P. Di Francesco The $q$-characters of representations of quantum affine algebras and deformations of $\mathcal W$-algebras by E. Frenkel and N. Reshetikhin Melzer's identities revisited by O. Foda and T. A. Welsh Automorphisms of lattice type vertex operator algebras and variations, a survey by R. L. Griess, Jr. Remarks on fermionic formula by G. Hatayama, A. Kuniba, M. Okado, T. Takagi, and Y. Yamada $q$-vertex operators for quantum affine algebras by N. Jing and K. C. Misra Homology of certain truncated Lie algebras by S. Kumar Vertex operator algebras and the zeta function by J. Lepowsky On $\mathbb Z$-graded associative algebras and their $\mathbb N$-graded modules by H. Li and S. Wang An $\mathbb A$-form technique of quantum deformations by D. J. Melville Determinant formula for the solutions of the quantum Knizhnik-Zamolodchikov equation with $q=1$ by T. Miwa and Y. Takeyama Functorial properties of the hypergeometric map by E. Mukhin and A. Varchenko Polyhedral realizations of crystal bases and braid-type isomorphisms by T. Nakashima Meromorphic tensor categories, quantum affine and chiral algebras I by Y. Soibelman Dual pairs and infinite dimensional Lie algebras by W. Wang.}, publisher={Providence, RI: American Mathematical Society}, author={Jing, Naihuan and Misra, K. C.}, year={1999} }
 @article{jing_misra_1999, title={Vertex operators for twisted quantum affine algebras}, volume={351}, ISSN={["0002-9947"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-22644451731&partnerID=MN8TOARS}, DOI={10.1090/S0002-9947-99-02098-X}, abstractNote={We construct explicitly the q-vertex operators (intertwining operators) for the level one modules V (�i) of the classical quantum affine algebras of twisted types using interacting bosons, where i = 0,1 for A (2)n−1, i = 0 for D (3) , i = 0, n for D (2)+1, and i = n for A (2)n . A perfect crystal graph for D (3) 4 is constructed as a by-product.}, number={4}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Jing, NH and Misra, KC}, year={1999}, month={Apr}, pages={1663–1690} }
 @article{jing_koyama_misra_1998, title={Bosonic realizations of U-q(C-n((1)))}, volume={200}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0039993885&partnerID=MN8TOARS}, DOI={10.1006/jabr.1997.7227}, abstractNote={Abstract We construct explicitly the quantum symplectic affine algebraUq( sp 2n) using bosonic fields. The Fock space decomposes into irreducible modules of level −1/2, quantizing the Feingold–Frenkel construction forq = 1.}, number={1}, journal={JOURNAL OF ALGEBRA}, author={Jing, NH and Koyama, Y and Misra, KC}, year={1998}, month={Feb}, pages={155–172} }
 @article{beck_frenkel_jing_1998, title={Canonical basis and Macdonald polynomials}, volume={140}, ISSN={["0001-8708"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0039657295&partnerID=MN8TOARS}, DOI={10.1006/aima.1998.1763}, abstractNote={Abstract In the basic representation of[formula]realized via the algebra of symmetric functions, we compare the canonical basis with the basis of Macdonald polynomials where t = q 2 . We show that the Macdonald polynomials are invariant with respect to the bar involution defined abstractly on the representations of quantum groups. We also prove that the Macdonald scalar product coincides with the abstract Kashiwara form. This implies, in particular, that the Macdonald polynomials form an intermediate basis between the canonical basis and the dual canonical basis, and the coefficients of the transition matrix are necessarily bar invariant. We also verify that the Macdonald polynomials (after a natural rescaling) form a sublattice in the canonical basis lattice which is invariant under the divided powers action. The transition matrix with respect to this rescaling is integral and we conjecture its positivity. For level k , we expect a similar relation between the canonical basis and Macdonald polynomials with q 2 = t k .}, number={1}, journal={ADVANCES IN MATHEMATICS}, author={Beck, J and Frenkel, IB and Jing, NH}, year={1998}, month={Dec}, pages={95–127} }
 @article{jing_1998, title={Quantum Kac-Moody Algebras and Vertex Representations}, volume={44}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001302342&partnerID=MN8TOARS}, DOI={10.1023/a:1007493921464}, number={4}, journal={Letters in Mathematical Physics}, author={Jing, N.}, year={1998}, pages={261–271} }
 @article{jing_koyama_1998, title={Vertex operators of admissible modules of U-q(C-n((1)))}, volume={205}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0039413629&partnerID=MN8TOARS}, DOI={10.1006/jabr.1997.7407}, abstractNote={Using our recent bosonic realization ofUq(Sp2n), we construct explicitly the vertex operators for the level −1/2 modules ofUq(Sp2n) using bosonic fields. Our method contains a detailed analysis of all theq-intertwining relations.}, number={1}, journal={JOURNAL OF ALGEBRA}, author={Jing, NH and Koyama, Y}, year={1998}, month={Jul}, pages={294–316} }
 @article{jing_zhang_1997, title={On the trace of graded automorphisms}, volume={189}, ISSN={["0021-8693"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0031569313&partnerID=MN8TOARS}, DOI={10.1006/jabr.1996.6896}, abstractNote={Abstract LetA = ⊕d ≥ 0 Adbe a connected algebra with a graded algebra endomorphism σ. The trace of σ is defined to be Tr(σ, t) = ∑d ≥ 0 tr(σ|Ad)td. We prove that Tr(σ, t) is a rational function ifAis either finitely generated commutative or right noetherian with finite global dimension or regular. A version of Molien's theorem follows in these three cases. IfAis a regular algebra or a Frobenius algebra we prove a reciprocity for the trace. We also partially generalize a theorem of Watanabe on the Gorenstein property to the noncommutative case.}, number={2}, journal={JOURNAL OF ALGEBRA}, author={Jing, NH and Zhang, JJ}, year={1997}, month={Mar}, pages={353–376} }
 @article{jing_1996, title={Higher level representations of the quantum affine algebra Uq(ŝl(2))}, volume={182}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030167072&partnerID=MN8TOARS}, DOI={10.1006/jabr.1996.0180}, abstractNote={Abstract We introduce the notion of quantum Z-algebras for the quantum affine algebra. After developing the quantum Z-algebra we use it to study the quantum affine algebraUq(sl(2)) and construct bases for each of its higher level modules.}, number={2}, journal={Journal of Algebra}, author={Jing, N.}, year={1996}, pages={448–468} }
 @article{jing_misra_1996, title={Vertex Operators of Level-One UqBn (1)-modules}, volume={36}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0039319607&partnerID=MN8TOARS}, number={2}, journal={Letters in Mathematical Physics}, author={Jing, N. and Misra, K.C.}, year={1996}, pages={127–143} }
 @article{jing_1995, title={Boson-fermion correspondence for Hall-Littlewood polynomials}, volume={36}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-21844499602&partnerID=MN8TOARS}, number={12}, journal={Journal of Mathematical Physics}, author={Jing, N.}, year={1995}, pages={7073–7080} }
 @article{jing_kang_koyama_1995, title={Vertex operators of quantum affine Lie algebras Uq(Dn (1))}, volume={174}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000124645&partnerID=MN8TOARS}, DOI={10.1007/BF02099607}, abstractNote={We give an explicit formula for the vertex operators related to the level 1 representations of the quantum affine Lie algebrasU q (D (1) ) in terms of bosons. As an application, we derive an integral formula for the correlation functions of the vertex models withU q (D (1) )-symmetry.}, number={2}, journal={Communications in Mathematical Physics}, author={Jing, N. and Kang, S.-J. and Koyama, Y.}, year={1995}, pages={367–392} }
 @article{ge_jing_liu_1992, title={On quantum groups for ZN models}, volume={25}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-36149029393&partnerID=MN8TOARS}, DOI={10.1088/0305-4470/25/13/007}, abstractNote={The quantum group for the ZN model is studied from the braid group representation. The fundamental representation is constructed from the Weyl relation ZX= omega XZ with omega being an Nth root of unity. In the case of N=2 (the eight vertex model), the quantum group is shown to be a homomorphic image of the GLq(2) with q2=1.}, number={13}, journal={Journal of Physics A: Mathematical and General}, author={Ge, M.-L. and Jing, N.-H. and Liu, G.-Q.}, year={1992} }
 @article{jing_ge_wu_1991, title={A new quantum group associated with a 'nonstandard' braid group representation}, volume={21}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0002346824&partnerID=MN8TOARS}, DOI={10.1007/BF00420369}, abstractNote={A new quantum group is derived from a ‘nonstandard’ braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x 2−y 2=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.}, number={3}, journal={Letters in Mathematical Physics}, author={Jing, N. and Ge, M.-L. and Wu, Y.-S.}, year={1991}, pages={193–203} }
 @article{jing_1991, title={Vertex operators and Hall-Littlewood symmetric functions}, volume={87}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001443775&partnerID=MN8TOARS}, DOI={10.1016/0001-8708(91)90072-F}, abstractNote={We consider vertex operators on space V with a parameter t. Their components form an associative algebra which is a generalization of the Clifford algebra. A distinguished orthogonal basis of V is proved to be the Hall-Littlewood symmetric functions. We show that Kostka-Foulkes polynomials (or certain Kazhdan-Lusztig polynomials for the affine Weyl group of type A) are matrix coefficients on the space V. We also obtain certain generating functions for the product of Hall-Littlewood functions and the Kostka-Foulkes polynomials.}, number={2}, journal={Advances in Mathematics}, author={Jing, N.}, year={1991}, pages={226–248} }
 @article{jing_1991, title={Vertex operators, symmetric functions, and the spin group Γn}, volume={138}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0001056353&partnerID=MN8TOARS}, DOI={10.1016/0021-8693(91)90177-A}, abstractNote={This work provides a vertex operator approach to the symmetric group Sn and its double covering group Γn. By generalizing a result of Frenkel and Sato for Sn we formulate a correspondence between the space V̂ of certain twisted vertex operators, the ring Λ of symmetric functions over Q(√2), and the space of nontrivial irreducible characters of Γn. Under this identification we show that a distinguished orthogonal basis of V̂ corresponds to the set of nontrivial irreducible characters of Γn, where both are parametrized by partitions with odd integer parts. The counterpart of this distinguished basis in the ring Λ over Q(√2) is the set of Schur's Q-functions, which are, loosely speaking, the square roots of the Schur functions. The nontrivial part of the character table of Γn is shown to be given by certain matrix coefficients in V̂.}, number={2}, journal={Journal of Algebra}, author={Jing, N.}, year={1991}, pages={340–398} }
 @article{jing_1990, title={Twisted vertex representations of quantum affine algebras}, volume={102}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0000572295&partnerID=MN8TOARS}, DOI={10.1007/BF01233443}, abstractNote={Recent interests in quantum groups are stimulated by their marvelous relations with quantum Yang-Baxter equations, conformal field theory, invariants of links and knots, and q-hypergeometric series. Besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q-deformations or quantum analogues of known structures. Quantum groups were first defined by Drinfeld [2] and Jimbo [9] (also see [4]) as a q-deformation of the universal enveloping algebras of the KacMoody algebras in the work of trigonometric solutions of Yang-Baxter equations. In the same spirit it was shown in [13], [14], that there exists a 1 1 correspondence between the integrable highest weight representations of symmetrizable Kac-Moody algebras and those of the corresponding quantum groups, where both spaces have the same dimension in the case of generic q (i.e. q is not a root of unity). Moreover, one can be very explicit in the case of quantum gl(n) to write down the irreducible highest weight representations. Quantum affine algebras are the quantum groups associated to affine Lie algebras. Following Drinfeld's realization [-3] of q-analog of loop algebras, the vertex representation of untwisted simply laced quantum affine algebras was constructed in Frenkel-Jing [6], which is a q-deformation of Frenkel-Kac [7] and Segal [15] construction in the theory of affine Lie algebras. Subsequently, the same was done for the quantum affine algebra of type B in [1]. In the present work we construct vertex representations of quantum affine algebras twisted by an automorphism of the Dynkin diagram, which generalizes certain important cases in the ordinary twisted vertex operator calculus [-5,}, number={1}, journal={Inventiones Mathematicae}, author={Jing, N.}, year={1990}, pages={663–690} }