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Works (31)
Updated: April 4th, 2024 22:45
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 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
2014 journal article
Cauchy problems related to integrable deformations of pseudo differential operators
JOURNAL OF GEOMETRY AND PHYSICS, 85, 196–205.
author keywords: Cauchy problem; Integrable deformation; Pseudo differential operators; (Strict) KP hierarchy; Zero curvature relations
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
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.
author keywords: Lower triangular Z x Z-matrices; Lax equations; Zero curvature form; Linearization; Wave matrices
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2013 journal article
Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective
THEORETICAL AND MATHEMATICAL PHYSICS, 174(1), 134–153.
author keywords: integrable deformation; pseudodifferential operator; Lax equation; Kadomtsev-Petviashvili hierarchy; zero-curvature relation; linearization
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
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.
author keywords: symmetric spaces; symbolic computation
citeseerx.ist.psu.edu (repository)
Source: Web Of Science
Added: August 6, 2018
2011 journal article
Admissible Sequences for Twisted Involutions in Weyl Groups
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 54(4), 663–675.
Source: Web Of Science
Added: August 6, 2018
2011 journal article
Equivalent forms of multi component Toda hierarchies
JOURNAL OF GEOMETRY AND PHYSICS, 61(4), 847–873.
author keywords: Lower and upper triangular Z x Z-matrices; Infinite dimensional Cauchy problem; Lax equations; Zero curvature form; Bilinear form
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
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.
author keywords: Lower and upper triangular Z x Z-matrices; Infinite dimensional Cauchy problem; Lax equations; Zero curvature form; Bilinear form
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2011 journal article
On generalized Cartan subspaces
TRANSFORMATION GROUPS, 16(3), 783–805.
Source: Web Of Science
Added: August 6, 2018
2010 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
Source: Web Of Science
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.
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)
Source: Web Of Science
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.
author keywords: k-split tori; Minimal parabolic subgroups; p-adic numbers; Symmetric k-varieties; Symmetric spaces
Source: Web Of Science
Added: August 6, 2018
2009 journal article
Real double coset spaces and their invariants
JOURNAL OF ALGEBRA, 322(1), 219–236.
author keywords: Symmetric spaces; Symmetric varieties; Cartan subspaces
Source: Web Of Science
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)
Source: Web Of Science
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)
Source: Web Of Science
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)
Source: Web Of Science
Added: August 6, 2018
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
Source: Web Of Science
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
Source: Web Of Science
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.
Source: Web Of Science
Added: August 6, 2018
2002 journal article
Classification of involutions of SL(2, k)
COMMUNICATIONS IN ALGEBRA, 30(1), 193–203.
Source: Web Of Science
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.
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
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.
author keywords: symmetric variety; symmetric subgroup; spherical subgroup
Source: Web Of Science
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
Source: Web Of Science
Added: August 6, 2018
2001 journal article
Orbits and invariants associated with a pair of commuting involutions
DUKE MATHEMATICAL JOURNAL, 106(2), 237–279.
Source: Web Of Science
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.
TL;DR:
This paper presents an algorithm to compute the orbits of a minimal parabolic k -subgroup acting on a symmetric k -variety and most of the combinatorial structure of the orbit decomposition and shows how the algorithm in Helminck (1996) can be adjusted and extended to compute these twisted involutions.
(via Semantic Scholar)
Source: Web Of Science
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.
Source: Web Of Science
Added: August 6, 2018
2000 journal article
On the classification of k-involutions
ADVANCES IN MATHEMATICS, 153(1), 1–117.
author keywords: symmetric spaces; symmetric varieties; k-involutions
Source: Web Of Science
Added: August 6, 2018
1999 journal article
A conjugacy theorem for symmetric spaces
MATHEMATISCHE ANNALEN, 313(4), 785–791.
Source: Web Of Science
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.
Source: Web Of Science
Added: August 6, 2018
1997 journal article
Tori invariant under an involutorial automorphism .2.
ADVANCES IN MATHEMATICS, 131(1), 1–92.
Source: Web Of Science
Added: August 6, 2018
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