Aloysius G Helminck

A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian Z×Z-matrices

Indagationes Mathematicae.

Classifying the orbits of the generalized symmetric spaces for

Communications in Algebra, 48(4), 1744–1757.

Extended symmetric spaces and θ-twisted involution graphs

Communications in Algebra, 48(6), 2293–2306.

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.

Erratum of "Isomorphy classes of involutions of SP(2n, k), n &gt; 2"

Journal of Lie Theory, 26(1), 293–295. http://www.scopus.com/inward/record.url?eid=2-s2.0-84955487887&partnerID=MN8TOARS

Isomorphy classes of involutions of SO(n, k, beta), n > 2

Isomorphy classes of involutions of SO(n, k, beta), n > 2. Journal of Lie Theory, 26(2), 383–438.

Isomorphy classes of involutions of SO(n, κ, β), n &gt; 2

Journal of Lie Theory, 26(2), 383–438. http://www.scopus.com/inward/record.url?eid=2-s2.0-84983329156&partnerID=MN8TOARS

Isomorphy classes of involutions of SP(2n, k), n > 2 (vol 25, pg 903, 2015)

Isomorphy classes of involutions of SP(2n, k), n > 2 (vol 25, pg 903, 2015). Journal of Lie Theory, Vol. 26, pp. 293–295.

Isomorphy classes of involutions of SP(2n, k), n &gt; 2

Journal of Lie Theory, 25(4), 903–947. http://www.scopus.com/inward/record.url?eid=2-s2.0-84929886770&partnerID=MN8TOARS

Cauchy problems related to integrable deformations of pseudo differential operators

JOURNAL OF GEOMETRY AND PHYSICS, 85, 196–205.

Infinite dimensional symmetric spaces and Lax equations compatible with the infinite Toda chain

JOURNAL OF GEOMETRY AND PHYSICS, 85, 60–74.

On the structure of involutions and symmetric spaces of dihedral groups

Note Di Matematica, 34(2), 23–40.

Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective

THEORETICAL AND MATHEMATICAL PHYSICS, 174(1), 134–153.

Algorithms for Twisted Involutions in Weyl Groups

Haas, R., & Helminck, A. G. (2012, June). ALGEBRA COLLOQUIUM, Vol. 19, pp. 263–282.

Permutation notations for the exceptional Weyl groupF4

Involve, a Journal of Mathematics, 5(1), 81–89.

Admissible Sequences for Twisted Involutions in Weyl Groups

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 54(4), 663–675.

Dedication to Gerardus F. Helminck

Journal of Geometry and Physics, 61(9), 1631.

Editors' preface for the topical issue on "The interface between integrability and quantization"

Journal of Geometry and Physics, 61(9), 1632.

Equivalent forms of multi component Toda hierarchies

JOURNAL OF GEOMETRY AND PHYSICS, 61(4), 847–873.

Equivalent forms of multi component Toda hierarchies (Reprinted from JOURNAL OF GEOMETRY AND PHYSICS, vol 61, pg 847, 2011)

Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2011, September). JOURNAL OF GEOMETRY AND PHYSICS, Vol. 61, pp. 1755–1781.

On generalized Cartan subspaces

TRANSFORMATION GROUPS, 16(3), 783–805.

THE RELATIVE FRAME BUNDLE OF AN INFINITE-DIMENSIONAL FLAG VARIETY AND SOLUTIONS OF INTEGRABLE HIERARCHIES

THEORETICAL AND MATHEMATICAL PHYSICS, 165(3), 1610–1636.

On Orbit Decompositions for Symmetric k-Varieties

SYMMETRY AND SPACES, Vol. 278, pp. 83–127.

On the Classification of Orbits of Symmetric Subgroups Acting on Flag Varieties of SL(2, k)

COMMUNICATIONS IN ALGEBRA, 37(4), 1334–1352.

Real double coset spaces and their invariants

JOURNAL OF ALGEBRA, 322(1), 219–236.

Algorithms for computations in local symmetric spaces

COMMUNICATIONS IN ALGEBRA, 36(5), 1758–1788.

Algorithms for computing characters for symmetric spaces

Gagliardi, D., & Helminck, A. G. (2007, December). ACTA APPLICANDAE MATHEMATICAE, Vol. 99, pp. 339–365.

Computing the fine structure of real reductive symmetric spaces

JOURNAL OF SYMBOLIC COMPUTATION, 42(5), 497–510.

Properties of twisted involutions in signed permutation notation

Journal of Combinatorial Mathematics and Combinatorial Computing, 62, 121–128. http://www.scopus.com/inward/record.url?eid=2-s2.0-78651544802&partnerID=MN8TOARS

Implementation of algorithms for computing characters for symmetric spaces

Congr. Numer., 180, 5–20.

Implementing an algorithm for the twisted involution poset for Weyl groups

Congr. Numer., 182, 137–144.

Involutions of SL(n,k), (n < 2)

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.

Multiplicity one for representations corresponding to spherical distribution vectors of class rho

Helminck, A. G., & Helminck, G. F. (2005, March). ACTA APPLICANDAE MATHEMATICAE, Vol. 86, pp. 21–48.

Smoothness of quotients associated with a pair of commuting involutions

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 56(5), 945–962.

Classification of involutions of SL(2, k)

COMMUNICATIONS IN ALGEBRA, 30(1), 193–203.

Hilbert flag varieties and their Kahler structure

Helminck, G. F., & Helminck, A. G. (2002, October 11). JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, Vol. 35, pp. 8531–8550.

Orbits and invariants associated with a pair of spherical varieties: Some examples

Helminck, A. G., & Schwarz, G. W. (2002, August). ACTA APPLICANDAE MATHEMATICAE, Vol. 73, pp. 103–113.

Spherical distribution vectors

Helminck, A. G., & Helminck, G. F. (2002, August). ACTA APPLICANDAE MATHEMATICAE, Vol. 73, pp. 39–57.

Orbits and invariants associated with a pair of commuting involutions

DUKE MATHEMATICAL JOURNAL, 106(2), 237–279.

Computing orbits of minimal parabolic k-subgroups acting on symmetric k-varieties

JOURNAL OF SYMBOLIC COMPUTATION, 30(5), 521–553.

On orbit closures of symmetric subgroups in flag varieties

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 52(2), 265–292.

On the classification of k-involutions

ADVANCES IN MATHEMATICS, 153(1), 1–117.

A conjugacy theorem for symmetric spaces

MATHEMATISCHE ANNALEN, 313(4), 785–791.

A class of parabolic k-subgroups associated with symmetric k-varieties

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 350(11), 4669–4691.

Tori invariant under an involutorial automorphism .2.

ADVANCES IN MATHEMATICS, 131(1), 1–92.

Computing B-orbits on G/H

Journal of Symbolic Computation, 21(2), 169–209.

Infinite-dimensional flag manifolds in integrable systems

Acta Applicandae Mathematicae, 41(1-3), 99–121.

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.

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.

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.

On rationality properties of involutions of reductive groups

Advances in Mathematics, 99(1), 26–96.

On groups with a Cartan involution

Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), 151–192. Manoj Prakashan, Madras.

Tori invariant under an involutorial automorphism, I

Advances in Mathematics, 85(1), 1–38.

On the orbits of symmetric spaces under the action of parabolic subgroups

Invariant Theory, 435–447.

Algebraic groups with a commuting pair of involutions and semisimple symmetric spaces

Advances in Mathematics, 71(1), 21–91.

Trilinear alternating forms on a vector space of dimension 7

Communications in Algebra, 16(1), 1–25.

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.

The structure of real semisimple Lie groups

(Vol. 49, p. v+141). Mathematisch Centrum, Amsterdam.

On the structure of generalized symmetric spaces of SL<inf>n</inf>F<inf>q</inf>)

Communications in Algebra, 45(12), 5123–5136.