Characterizations of character sheaves for complex reductive algebraic groups
type: Item
instance of: scholarly article
title: Characterizations of character sheaves for complex reductive algebraic groups
zbMATH Open document ID: 0831.20055
DOI: 10.1215/S0012-7094-95-07703-5
author: E. Galaktionova
published in: Duke Mathematical Journal
publication date: 1995-01-01T00:00:00Z
review text: Let \(G\) be a connected complex reductive algebraic group. As the introduction explains, several definitions of character sheaves have been around. Here the situation is clarified (at least over the complex numbers). Identifying the tangent bundle of \(G\) with the cotangent bundle, we may think of the microsupport \(SS({\mathcal F})\) of a \(G\)- equivariant perverse sheaf \(\mathcal F\) on \(G\) as lying in the tangent bundle. The author now characterizes character sheaves by the property that their microsupport lies in the nullcone part of the tangent bundle. This criterion comes in five variations, depending on whether one looks at the elements of \(G\), conjugacy classes in \(G\), the set of semisimple elements of \(G\) \dots The characterization is also compared with Lusztig's original description of character sheaves, where the building block is the intersection cohomology complex of an irreducible \(G\)- equivariant local system on a \(G\)-orbit close to the zero section in the normal bundle of a semisimple conjugacy class. There is an appendix on microsupport of constructible sheaves in the presence of a group action.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 755404
zbMATH Keywords: connected complex reductive algebraic group
zbMATH Keywords: character sheaves
zbMATH Keywords: microsupport
zbMATH Keywords: \(G\)-equivariant perverse sheaf
zbMATH Keywords: tangent bundle
zbMATH Keywords: semisimple elements
zbMATH Keywords: intersection cohomology
zbMATH Keywords: constructible sheaves
zbMATH Keywords: group action
reviewed by: Wilberd van der Kallen
MaRDI profile type: Publication
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full work available at URL: s0012-7094-95-07703-5
OpenAlex ID: W1596486749
description: scientific article; zbMATH DE number 755404