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

DOI10.1006/jsco.2000.0395zbMath0982.20031OpenAlexW1997241288MaRDI QIDQ5926298

Aloysius G. Helminck

Publication date: 17 December 2001

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.2000.0395

zbMATH Keywords

algorithmsminimal parabolic subgroupsorbitssymmetric varieties

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Homogeneous spaces and generalizations (14M17) Linear algebraic groups over arbitrary fields (20G15) Group actions on varieties or schemes (quotients) (14L30)

Related Items

Algorithms for Twisted Involutions in Weyl Groups, Extended symmetric spaces and θ-twisted involution graphs, Algorithms for Computations in Local Symmetric Spaces, Modules with Involution for Algebraic Groups

Uses Software

• LiE
• coxeter

Cites Work

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• Elliptic genera, involutions, and homogeneous spin manifolds
• Singularities of closures of K-orbits on flag manifolds
• Tori invariant under an involutorial automorphism. I
• The Bruhat order on symmetric varieties
• Eigenspaces of invariant differential operators on an affine symmetric space
• Discrete series for semisimple symmetric spaces
• Finiteness of orbit structure for real flag manifolds
• The orbits of affine symmetric spaces under the action of minimal parabolic subgroups
• On a remarkable class of subvarieties of a symmetric variety
• A trace formula for symmetric spaces
• A finiteness property and an automatic structure for Coxeter groups
• Machine calculations in Weyl groups
• The most continuous part of the Plancherel decomposition for a reductive symmetric space
• Tori invariant under an involutorial automorphism. II
• On the classification of \(k\)-involutions
• \(H\)-fixed distribution vectors for generalized principal series of reductive symmetric spaces and meromorphic continuation of Eisenstein integrals
• Algebraic groups with a commuting pair of involutions and semisimple symmetric spaces
• Geometric realization of discrete series for semisimple symmetric spaces
• Irreducible characters of semisimple Lie groups. III: Proof of Kazhdan-Lusztig conjecture in the integral case
• Orbits, invariants, and representations associated to involutions of reductive groups
• Orbits and invariants associated with a pair of commuting involutions
• Computing \(B\)-orbits on \(G/H\)
• On rationality properties of involutions of reductive groups
• Groupes reductifs
• Complements à l'article: Groupes reductifs
• The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors
• The Structure of Semisimple Symmetric Spaces
• A class of parabolic $k$-subgroups associated with symmetric $k$-varieties
• Weyl group orbits
• On Orbit Closures of Symmetric Subgroups in Flag Varieties
• Spherical Characters on p-Adic Symmetric Spaces
• Endomorphisms of linear algebraic groups
• Linear algebraic groups.