Aloysius Helminck

Helminck, A. G., & Helminck, G. F. (2025). A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian Z×Z-matrices. Indagationes Mathematicae. https://doi.org/10.1016/j.indag.2024.04.001

Buell, C., Helminck, A., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2025). Orbits of unipotent elements in the generalized symmetric space defined by inner involutions of SL3(𝔽q) and SL4(𝔽q) for q = 2n. Journal of Algebra and Its Applications. https://doi.org/10.1142/S0219498826501355

Buell, C., Helminck, A., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2020). Classifying the orbits of the generalized symmetric spaces for. Communications in Algebra, 48(4), 1744–1757. https://doi.org/10.1080/00927872.2019.1705471

Collins, J. B., Haas, R., Helminck, A. G., Lenarz, J., Pelatt, K. E., Saccon, S., & Welz, M. (2020). Extended symmetric spaces and θ-twisted involution graphs. Communications in Algebra, 48(6), 2293–2306. https://doi.org/10.1080/00927872.2019.1711106

Buell, C., Helminck, A. G., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2017). On the structure of generalized symmetric spaces of SL<inf>2</inf>(F<inf>q</inf>) and GL<inf>2</inf>(F<inf>q</inf>). Note Di Matematica, 37(2), 1–10. https://doi.org/10.1285/i15900932v37n2p1

Buell, C., Helminck, A., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2017). On the structure of generalized symmetric spaces of SL<inf>n</inf>F<inf>q</inf>). Communications in Algebra, 45(12), 5123–5136. https://doi.org/10.1080/00927872.2017.1296458

Benim, R. W., Helminck, A. G., & Ward, F. J. (2016). Erratum of "Isomorphy classes of involutions of SP(2n, k), n > 2". Journal of Lie Theory, 26(1), 293–295. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-84955487887&partnerID=MN8TOARS

Benim, R. W., Dometrius, C. E., Helminck, A. G., & Wu, L. (2016). Isomorphy classes of involutions of SO(n, k, beta), n > 2. Journal of Lie Theory, 26(2), 383–438.

Benim, R. W., Dometrius, C. E., Helminck, A. G., & Wu, L. (2016). Isomorphy classes of involutions of SO(n, κ, β), n > 2. Journal of Lie Theory, 26(2), 383–438. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-84983329156&partnerID=MN8TOARS

Benim, R. W., Helminck, A. G., & Ward, F. J. (2016). Isomorphy classes of involutions of SP(2n, k), n > 2 (vol 25, pg 903, 2015). Journal of Lie Theory, Vol. 26, pp. 293–295.

Benim, R. W., Helminck, A. G., & Ward, F. J. (2015). Isomorphy classes of involutions of SP(2n, k), n > 2. Journal of Lie Theory, 25(4), 903–947. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-84929886770&partnerID=MN8TOARS

Helminck, G. F., Helminck, A. G., & Panasenko, E. A. (2014). Cauchy problems related to integrable deformations of pseudo differential operators. JOURNAL OF GEOMETRY AND PHYSICS, 85, 196–205. https://doi.org/10.1016/j.geomphys.2014.05.004

Helminck, G. F., & Helminck, A. G. (2014). Infinite dimensional symmetric spaces and Lax equations compatible with the infinite Toda chain. JOURNAL OF GEOMETRY AND PHYSICS, 85, 60–74. https://doi.org/10.1016/j.geomphys.2014.05.023

Cunningham, K. K. A., Edgar, T., Helminck, A. G., Jones, B. F., Oh, H., Schwell, R., & Vasquez, J. F. (2014). On the structure of involutions and symmetric spaces of dihedral groups. Note Di Matematica, 34(2), 23–40. https://doi.org/10.1285/i15900932v34n2p23

Helminck, G. F., Helminck, A. G., & Panasenko, E. A. (2013). Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective. THEORETICAL AND MATHEMATICAL PHYSICS, 174(1), 134–153. https://doi.org/10.1007/s11232-013-0011-7

Haas, R., & Helminck, A. G. (2012, June). Algorithms for Twisted Involutions in Weyl Groups. ALGEBRA COLLOQUIUM, Vol. 19, pp. 263–282. https://doi.org/10.1142/s100538671200017x

Cahn, P., Haas, R., Helminck, A., Li, J., & Schwartz, J. (2012). Permutation notations for the exceptional Weyl groupF4. Involve, a Journal of Mathematics, 5(1), 81–89. https://doi.org/10.2140/involve.2012.5.81

Haas, R., & Helminck, A. G. (2011). Admissible Sequences for Twisted Involutions in Weyl Groups. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 54(4), 663–675. https://doi.org/10.4153/cmb-2011-075-1

Helminck, A. G., Krasil’shchik, J., & Rubtsov, V. (2011). Dedication to Gerardus F. Helminck. Journal of Geometry and Physics, 61(9), 1631. https://doi.org/10.1016/j.geomphys.2011.04.003

Helminck, A. G., Krasil’shchik, J., & Rubtsov, V. (2011). Editors' preface for the topical issue on "The interface between integrability and quantization". Journal of Geometry and Physics, 61(9), 1632. https://doi.org/10.1016/j.geomphys.2011.04.002

Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2011). Equivalent forms of multi component Toda hierarchies. JOURNAL OF GEOMETRY AND PHYSICS, 61(4), 847–873. https://doi.org/10.1016/j.geomphys.2010.11.013

Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2011, September). Equivalent forms of multi component Toda hierarchies (Reprinted from JOURNAL OF GEOMETRY AND PHYSICS, vol 61, pg 847, 2011). JOURNAL OF GEOMETRY AND PHYSICS, Vol. 61, pp. 1755–1781. https://doi.org/10.1016/j.geomphys.2011.06.012

Helminck, A. G., & Schwarz, G. W. (2011). On generalized Cartan subspaces. TRANSFORMATION GROUPS, 16(3), 783–805. https://doi.org/10.1007/s00031-011-9151-8

Helminck, A. G. (2010). On Orbit Decompositions for Symmetric k-Varieties. SYMMETRY AND SPACES, Vol. 278, pp. 83–127. https://doi.org/10.1007/978-0-8176-4875-6_6

Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2010). THE RELATIVE FRAME BUNDLE OF AN INFINITE-DIMENSIONAL FLAG VARIETY AND SOLUTIONS OF INTEGRABLE HIERARCHIES. THEORETICAL AND MATHEMATICAL PHYSICS, 165(3), 1610–1636. https://doi.org/10.1007/s11232-010-0133-0

Beun, S. L., & Helminck, A. G. (2009). On the Classification of Orbits of Symmetric Subgroups Acting on Flag Varieties of SL(2, k). COMMUNICATIONS IN ALGEBRA, 37(4), 1334–1352. https://doi.org/10.1080/00927870802466983

Helminck, A. G., & Schwarz, G. W. (2009). Real double coset spaces and their invariants. JOURNAL OF ALGEBRA, 322(1), 219–236. https://doi.org/10.1016/j.jalgebra.2009.01.028

Daniel, J. R., & Helminck, A. G. (2008). Algorithms for computations in local symmetric spaces. COMMUNICATIONS IN ALGEBRA, 36(5), 1758–1788. https://doi.org/10.1080/00927870801940434

Gagliardi, D., & Helminck, A. G. (2007, December). Algorithms for computing characters for symmetric spaces. ACTA APPLICANDAE MATHEMATICAE, Vol. 99, pp. 339–365. https://doi.org/10.1007/s10440-007-9171-5

Daniel, J. R., & Helminck, A. G. (2007). Computing the fine structure of real reductive symmetric spaces. JOURNAL OF SYMBOLIC COMPUTATION, 42(5), 497–510. https://doi.org/10.1016/j.jsc.2006.08.003

Haas, R., Helminck, A. G., & Rizki, N. (2007). Properties of twisted involutions in signed permutation notation. Journal of Combinatorial Mathematics and Combinatorial Computing, 62, 121–128. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-78651544802&partnerID=MN8TOARS

Gagliardi, D., & Helminck, A. G. (2006). Implementation of algorithms for computing characters for
              symmetric spaces. Congr. Numer., 180, 5–20.

Brenneman, K., Haas, R., & Helminck, A. G. (2006). Implementing an algorithm for the twisted involution poset for
              Weyl groups. Congr. Numer., 182, 137–144.

Helminck, A. G., Wu, L., & Dometrius, C. E. (2006, January). Involutions of SL(n,k), (n < 2). ACTA APPLICANDAE MATHEMATICAE, Vol. 90, pp. 91–119. https://doi.org/10.1007/s10440-006-9032-7

Helminck, A. G., & Helminck, G. F. (2005, March). Multiplicity one for representations corresponding to spherical distribution vectors of class rho. ACTA APPLICANDAE MATHEMATICAE, Vol. 86, pp. 21–48. https://doi.org/10.1007/s10440-005-0461-5

Helminck, A. G., & Schwarz, G. W. (2004). Smoothness of quotients associated with a pair of commuting involutions. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 56(5), 945–962. https://doi.org/10.4153/CJM-2004-043-7

Helminck, A. G., & Wu, L. (2002). Classification of involutions of SL(2, k). COMMUNICATIONS IN ALGEBRA, 30(1), 193–203. https://doi.org/10.1081/AGB-120006486

Helminck, G. F., & Helminck, A. G. (2002, October 11). Hilbert flag varieties and their Kahler structure. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, Vol. 35, pp. 8531–8550. https://doi.org/10.1088/0305-4470/35/40/312

Helminck, A. G., & Schwarz, G. W. (2002, August). Orbits and invariants associated with a pair of spherical varieties: Some examples. ACTA APPLICANDAE MATHEMATICAE, Vol. 73, pp. 103–113. https://doi.org/10.1023/A:1019726804264

Helminck, A. G., & Helminck, G. F. (2002, August). Spherical distribution vectors. ACTA APPLICANDAE MATHEMATICAE, Vol. 73, pp. 39–57. https://doi.org/10.1023/A:1019762302447

Helminck, A. G., & Schwarz, G. W. (2001). Orbits and invariants associated with a pair of commuting involutions. DUKE MATHEMATICAL JOURNAL, 106(2), 237–279. https://doi.org/10.1215/s0012-7094-01-10622-4

Helminck, A. G. (2000). Computing orbits of minimal parabolic k-subgroups acting on symmetric k-varieties. JOURNAL OF SYMBOLIC COMPUTATION, 30(5), 521–553. https://doi.org/10.1006/jsco.2000.0395

Brion, M., & Helminck, A. G. (2000). On orbit closures of symmetric subgroups in flag varieties. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 52(2), 265–292. https://doi.org/10.4153/CJM-2000-012-9

Helminck, A. G. (2000). On the classification of k-involutions. ADVANCES IN MATHEMATICS, 153(1), 1–117. https://doi.org/10.1006/aima.1998.1884

Helminck, A. G., Hilgert, J., Neumam, A., & Olafsson, G. (1999). A conjugacy theorem for symmetric spaces. MATHEMATISCHE ANNALEN, 313(4), 785–791. https://doi.org/10.1007/s002080050282

Helminck, A. G., & Helminck, G. F. (1998). A class of parabolic k-subgroups associated with symmetric k-varieties. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 350(11), 4669–4691. https://doi.org/10.1090/S0002-9947-98-02029-7

Helminck, A. G. (1997). Tori invariant under an involutorial automorphism .2. ADVANCES IN MATHEMATICS, 131(1), 1–92. https://doi.org/10.1006/aima.1997.1633

Helminck, A. G. (1996). Computing B-orbits on G/H. Journal of Symbolic Computation, 21(2), 169–209. https://doi.org/10.1006/jsco.1996.0008

Helminck, G. F., & Helminck, A. G. (1995). Infinite-dimensional flag manifolds in integrable systems. Acta Applicandae Mathematicae, 41(1-3), 99–121. https://doi.org/10.1007/BF00996107

Helminck, A. G., & Helminck, G. F. (1994). Holomorphic line bundles over Hilbert flag varieties. In Algebraic groups and their generalizations: quantum and
              infinite-dimensional methods (University Park, PA,
              1991) (Vol. 56, pp. 349–375). Amer. Math. Soc., Providence, RI.

Helminck, A. G. (1994). Symmetric $k$-varieties. In Algebraic groups and their generalizations: classical methods
              (University Park, PA, 1991) (Vol. 56, pp. 233–279). Amer. Math. Soc., Providence, RI.

Helminck, G. F., & Helminck, A. G. (1994). The Structure of Hilbert Flag Varieties Dedicated to the memory of our father. Publications of the Research Institute for Mathematical Sciences, 30(3), 401–441. https://doi.org/10.2977/prims/1195165905

Helminck, A. G., & Wang, S. P. (1993). On rationality properties of involutions of reductive groups. Advances in Mathematics, 99(1), 26–96. https://doi.org/10.1006/aima.1993.1019

Helminck, A. G. (1991). On groups with a Cartan involution. Proceedings of the Hyderabad Conference on Algebraic
              Groups (Hyderabad, 1989), 151–192. Manoj Prakashan, Madras.

Helminck, A. G. (1991). Tori invariant under an involutorial automorphism, I. Advances in Mathematics, 85(1), 1–38. https://doi.org/10.1016/0001-8708(91)90048-C

Helminck, A. G. (1989). On the orbits of symmetric spaces under the action of parabolic subgroups. Invariant Theory, 435–447. https://doi.org/10.1090/conm/088/999998

Helminck, A. G. (1988). Algebraic groups with a commuting pair of involutions and semisimple symmetric spaces. Advances in Mathematics, 71(1), 21–91. https://doi.org/10.1016/0001-8708(88)90066-7

Cohen, A. M., & Helminck, A. G. (1988). Trilinear alternating forms on a vector space of dimension 7. Communications in Algebra, 16(1), 1–25. https://doi.org/10.1080/00927878808823558

Helminck, A. G. (1986). A classification of semisimple symmetric pairs and their
              restricted root system. In Lie algebras and related topics (Windsor, Ont., 1984) (Vol. 5, pp. 333–340). Amer. Math. Soc., Providence, RI.

Koornwinder, T. H., Hoogenboom, B., Cohen, A. M., Vries, J., & Helminck, A. G. (1982). The structure of real semisimple Lie groups (Vol. 49, p. v+141). Mathematisch Centrum, Amsterdam.