Updated: August 8th, 2024 05:12

2024 journal article

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

*Indagationes Mathematicae*.

Source: ORCID

Added: August 8, 2024

2020 journal article

Classifying the orbits of the generalized symmetric spaces for

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

Contributors: C. Buell ^{*}, ^{*} , V. Klima ^{*}, J. Schaefer ^{*}, C. Wright ^{*} & E. Ziliak ^{*}

Source: ORCID

Added: August 8, 2024

2020 journal article

Extended symmetric spaces and θ-twisted involution graphs

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

Contributors: J. Collins^{*}, R. Haas ^{*}, ^{*} , J. Lenarz^{*}, K. Pelatt^{*}, S. Saccon^{*}, M. Welz ^{*}

Source: ORCID

Added: August 8, 2024

2018 journal article

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.

Source: ORCID

Added: August 8, 2024

2016 journal article

Erratum of "Isomorphy classes of involutions of SP(2n, k), n > 2"

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

Source: ORCID

Added: August 8, 2024

2016 journal article

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.

Source: NC State University Libraries

Added: August 6, 2018

2016 journal article

Isomorphy classes of involutions of SO(n, κ, β), n > 2

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

Source: ORCID

Added: August 8, 2024

2016 article

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.

Source: NC State University Libraries

Added: August 6, 2018

2015 journal article

Isomorphy classes of involutions of SP(2n, k), n > 2

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

Source: ORCID

Added: August 8, 2024

2014 journal article

Cauchy problems related to integrable deformations of pseudo differential operators

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

Contributors: G. Helminck ^{*}, ^{ n} & E. Panasenko

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2014 journal article

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

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

Contributors: G. Helminck ^{*} & ^{ n}

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2014 journal article

On the structure of involutions and symmetric spaces of dihedral groups

*Note Di Matematica*, *34*(2), 23–40.

Source: ORCID

Added: August 8, 2024

2013 journal article

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

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

Contributors: G. Helminck ^{*}, ^{ n} & E. Panasenko

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2012 article

Algorithms for Twisted Involutions in Weyl Groups

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

Contributors: R. Haas ^{*} & ^{ n}

author keywords: symmetric spaces; symbolic computation

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2012 journal article

Permutation notations for the exceptional Weyl groupF4

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

Source: ORCID

Added: August 8, 2024

2011 journal article

Admissible Sequences for Twisted Involutions in Weyl Groups

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

Contributors: R. Haas ^{*} & ^{ n}

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2011 journal article

Dedication to Gerardus F. Helminck

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

Source: ORCID

Added: August 8, 2024

2011 journal article

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

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

Source: ORCID

Added: August 8, 2024

2011 journal article

Equivalent forms of multi component Toda hierarchies

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

Contributors: G. Helminck ^{*}, ^{ n} & A. Opimakh

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2011 article

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.

Contributors: G. Helminck ^{*}, ^{ n} & A. Opimakh

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2011 journal article

On generalized Cartan subspaces

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

Contributors: ^{ n} & G. Schwarz ^{*}

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2010 journal article

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

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

Contributors: G. Helminck ^{*}, ^{ n} & A. Opimakh^{*}

author keywords: upper-triangular Z x Z matrices; Lax equations; zero curvature form

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2009 article

On Orbit Decompositions for Symmetric k-Varieties

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

author keywords: Symmetric spaces; symmetric varieties; involutions of algebraic groups

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2009 journal article

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

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2009 journal article

Real double coset spaces and their invariants

*JOURNAL OF ALGEBRA*, *322*(1), 219–236.

Contributors: ^{ n} & G. Schwarz ^{*}

author keywords: Symmetric spaces; Symmetric varieties; Cartan subspaces

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2008 journal article

Algorithms for computations in local symmetric spaces

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

author keywords: Lie algebras of linear algebraic groups; symmetric spaces

TL;DR:
This article lays the groundwork for computing the fine structure of symmetric spaces over the real numbers and other base fields, gives a complete set of algorithms for computing this structure and uses this to compute nice bases for the local symmetric varieties.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2007 article

Algorithms for computing characters for symmetric spaces

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

author keywords: symmetric spaces; Lie algebras of linear algebraic groups

TL;DR:
This paper considers the case that k is algebraically closed and gives explicit algorithmic formulas for expressing the characters of the weight lattice $\Lambda_{\mathfrak{a}}$ of the symmetric space in terms of the Characters of the Weight lattice of the group.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2007 journal article

Computing the fine structure of real reductive symmetric spaces

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

author keywords: symmetric spaces; Lie algebras of linear algebraic groups; computational Lie theory

TL;DR:
It is shown that this fine structure can be obtained from the setting of a complex reductive Lie group with a pair of commuting involutions, and a number of algorithms for computing the fine structure of the latter are given.
(via Semantic Scholar)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2007 journal article

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

Source: ORCID

Added: August 8, 2024

2006 conference paper

Implementation of algorithms for computing characters for symmetric spaces

*Congr. Numer.*, *180*, 5–20.

Source: ORCID

Added: August 8, 2024

2006 conference paper

Implementing an algorithm for the twisted involution poset for Weyl groups

*Congr. Numer.*, *182*, 137–144.

Source: ORCID

Added: August 8, 2024

2006 article

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.

author keywords: flag variety; symmetric subgroup

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2005 article

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.

author keywords: Hilbert subspace; distribution vector; spherical distribution; Plancherel formula

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2004 journal article

Smoothness of quotients associated with a pair of commuting involutions

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2002 journal article

Classification of involutions of SL(2, k)

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2002 article

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.

Contributors: G. Helminck ^{*} & ^{ n}

UN Sustainable Development Goal Categories

14. Life Below Water
(Web of Science)

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2002 article

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.

Contributors: ^{ n} & G. Schwarz ^{*}

author keywords: symmetric variety; symmetric subgroup; spherical subgroup

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2002 article

Spherical distribution vectors

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

author keywords: Hilbert subspace; distribution vector; spherical distribution; Plancherel formula

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2001 journal article

Orbits and invariants associated with a pair of commuting involutions

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2000 journal article

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

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2000 journal article

On orbit closures of symmetric subgroups in flag varieties

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

2000 journal article

author keywords: symmetric spaces; symmetric varieties; k-involutions

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

A conjugacy theorem for symmetric spaces

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

Contributors: ^{ n} , J. Hilgert ^{*}, A. Neumann^{*} & G. Ólafsson ^{*}

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

1998 journal article

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

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

1997 journal article

Tori invariant under an involutorial automorphism .2.

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

Sources: Web Of Science, NC State University Libraries, ORCID

Added: August 6, 2018

1996 journal article

UN Sustainable Development Goal Categories

4. Quality Education
(OpenAlex)

Source: ORCID

Added: August 8, 2024

1995 journal article

Infinite-dimensional flag manifolds in integrable systems

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

Contributors: G. Helminck ^{*} & ^{ n}

Source: ORCID

Added: August 8, 2024

1994 chapter

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.

Source: ORCID

Added: August 8, 2024

1994 chapter

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.

Source: ORCID

Added: August 8, 2024

1994 journal article

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.

Contributors: G. Helminck ^{ n} & ^{ n}

Source: ORCID

Added: August 8, 2024

1993 journal article

On rationality properties of involutions of reductive groups

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

Source: ORCID

Added: August 8, 2024

1991 conference paper

On groups with a Cartan involution

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

Source: ORCID

Added: August 8, 2024

1991 journal article

Tori invariant under an involutorial automorphism, I

*Advances in Mathematics*, *85*(1), 1–38.

Source: ORCID

Added: August 8, 2024

1989 conference paper

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

*Invariant Theory*, 435–447.

Source: ORCID

Added: August 8, 2024

1988 journal article

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

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

Source: ORCID

Added: August 8, 2024

1988 journal article

Trilinear alternating forms on a vector space of dimension 7

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

Source: ORCID

Added: August 8, 2024

1986 chapter

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.

Source: ORCID

Added: August 8, 2024

1982 book

The structure of real semisimple Lie groups

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

Source: ORCID

Added: August 8, 2024

journal article

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

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

Source: ORCID

Added: August 8, 2024

Updated: October 18th, 2020 22:00

2016 - present

1987 - 2016

1985 - 1987

Updated: October 18th, 2020 22:02

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