A remark on the orthogonality relations for Green functions
type: Item
instance of: scholarly article
title: A remark on the orthogonality relations for Green functions
zbMATH Open document ID: 0656.20046
DOI: 10.1016/0021-8693(86)90222-X
author: Tonny A. Springer
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let G be a connected linear algebraic group defined over the finite field \({\mathbb{F}}_ q\) of characteristic p. We denote by k an algebraic closure of \({\mathbb{F}}_ q\) and by F the Frobenius automorphism \((a\mapsto a^ q)\) of k over \({\mathbb{F}}_ q\). Then F operates on G and its group \(G^ F\) of fixed points is the finite group of \({\mathbb{F}}^ q\)-rational points of G. Now assume G to be reductive and let \({\mathcal U}\) be the \({\mathbb{F}}_ q\)- variety of unipotent elements of G. The Green functions of \(G^ F\) are class functions \(Q_{T,G}\) defined on the set \({\mathcal U}^ F\) of unipotent elements of \(G^ F\), parametrized by a maximal torus T of G defined over \({\mathbb{F}}_ q\) (and depending only on the \(G^ F\)-conjugacy class of T). They are of importance for the representation theory of \(G^ F\).
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 4071210
zbMATH Keywords: connected linear algebraic group
zbMATH Keywords: Frobenius automorphism
zbMATH Keywords: variety of unipotent elements
zbMATH Keywords: Green functions
zbMATH Keywords: class functions
zbMATH Keywords: representation
MaRDI profile type: Publication
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full work available at URL: 0021-8693(86)90222-x
OpenAlex ID: W2131502086
description: scientific article; zbMATH DE number 4071210