The Steinberg variety and representations of reductive groups.

DOI10.1016/j.jalgebra.2008.10.027zbMath1183.20044arXiv0802.0764OpenAlexW2963966378MaRDI QIDQ834827

J. Matthew Douglass, Gerhard Röhrle

Publication date: 27 August 2009

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0764

zbMATH Keywords

reductive algebraic groupsSpringer representationsSteinberg varieties

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Lie algebras of linear algebraic groups (17B45)

Related Items

Orbit embedding for double flag varieties and Steinberg maps, Borel-Moore homology and \(K\)-theory on the Steinberg variety, On irreducible representations of compact \(p\)-adic analytic groups, Irreducible components of exotic Springer fibres. II: The exotic Robinson-Schensted algorithm, FROM COMPLETE TO PARTIAL FLAGS IN GEOMETRIC EXTENSION ALGEBRAS, Conormal varieties on the cominuscule Grassmannian. II, Equivariant \(K\)-theory of generalized Steinberg varieties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cells in affine Weyl groups. II
• Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra. II.
• Intersection homology. II
• On the variety of a highest weight module
• Homology of the Steinberg variety and Weyl group coinvariants
• Differential operators on homogeneous spaces. III: Characteristic varieties of Harish Chandra modules and of primitive ideals
• \({\mathfrak G}\)-module, Springer's representations and bivariant Chern classes
• The characteristic cycles of holonomic systems on a flag manifold related to the Weyl group algebra
• Proof of the Deligne-Langlands conjecture for Hecke algebras
• An occurrence of the Robinson-Schensted correspondence
• Simple singularities and simple algebraic groups
• A topological approach to Springer's representations
• Classes unipotentes et sous-groupes de Borel
• Representations of Coxeter groups and Hecke algebras
• Nilpotent orbits, primitive ideals, and characteristic classes. A geometric perspective in ring theory
• A Lefschetz formula in equivariant algebraic \(K\)-theory
• On the desingularization of the unipotent variety
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• A construction of representations of Weyl groups
• Representations of affine Hecke algebras
• Sheaves in topology
• Differential operators on homogeneous spaces. I: Irreducibility of the associated variety for annihilators of induced modules
• The geometry of generalized Steinberg varieties.
• Environmentally induced amplitude death and firing provocation in large-scale networks of neuronal systems
• Orbital variety closures and the convolution product in Borel-Moore homology
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• An involution of the variety of flags fixed by a unipotent linear transformation
• Affine Hecke Algebras and Their Graded Version
• Characters of Reductive Groups over a Finite Field. (AM-107)
• Homology of generalized Steinberg varieties and Weyl group invariants
• A Two-Sided Cell in an Affine Weyl Group
• Dixmier's Problem for Verma and Principal Series Submodules
• Categorical framework for the study of singular spaces
• Bases in equivariant 𝐾-theory
• On the equivariant 𝐾-theory of the nilpotent cone
• Kazhdan-Lusztig Basis and a Geometric Filtration of an Affine Hecke Algebra
• Linear algebraic groups.