Symmetric subgroup invariants in irreducible representations of \(G^F\), when \(G=\text{GL}_n\)
type: Item
instance of: scholarly article
title: Symmetric subgroup invariants in irreducible representations of \(G^F\), when \(G=\text{GL}_n\)
zbMATH Open document ID: 1020.20030
DOI: 10.1016/S0021-8693(02)00559-8
author: Anthony Henderson
published in: Journal of Algebra
publication date: 2003-04-28T00:00:00Z
review text: In the mid 1980s, Lusztig classified the characteristic \(0\) irreducible representations of the fixed point subgroup \(G^F\) of a connected reductive group \(G\), defined over a finite field of odd characteristic, under the Frobenius morphism \(F\). In the paper under review, this is developed in the following way. It is supposed that there is an involution \(\theta\colon G\to G\) of algebraic groups which is assumed to commute with \(F\). Within the fixed-point subgroup \(G^\theta\), we take an \(F\)-stable subgroup \(K\). Then for each irreducible representation \(V\) of \(G^F\), it is desirable to find the dimension of the \(K^F\)-invariants in \(V\). The author achieves this in the case where \(G\) is a general linear group, and \(\theta\) is arbitrary.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 1901957
zbMATH Keywords: representation theory
zbMATH Keywords: linear algebraic groups
zbMATH Keywords: irreducible representations
zbMATH Keywords: connected reductive groups
zbMATH Keywords: invariants
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901957