A remark on irreducible modules for finite Lie-type groups
type: Item
instance of: scholarly article
title: A remark on irreducible modules for finite Lie-type groups
zbMATH Open document ID: 0603.20039
DOI: 10.1007/BF01195017
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let G be a finite group of Lie type, P a parabolic subgroup of G with unipotent radical M, K an algebraically closed field of prime characteristic, and V an irreducible KG-module. Using algebraic group methods, \textit{S. D. Smith} [J. Algebra 75, 286-289 (1982; Zbl 0496.20030)] has shown that if G is not of twisted type, then \(C_ V(M)\) is an irreducible module for P, so is a Levi complement. The author uses two results from the representation theory of groups of Lie type to construct a shorter and more general proof of this fact, one that establishes the result for G of twisted as well as of untwisted type.
reviewed by: James F. Hurley
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 3973163
zbMATH Keywords: Chevalley group
zbMATH Keywords: root system
zbMATH Keywords: Borel subgroup
zbMATH Keywords: finite group of Lie type
zbMATH Keywords: parabolic subgroup
zbMATH Keywords: unipotent radical
zbMATH Keywords: irreducible KG-module
zbMATH Keywords: twisted type
zbMATH Keywords: Levi complement
zbMATH Keywords: untwisted type
Wikidata QID: Q115393929
author: F. G. Timmesfeld
MaRDI profile type: Publication
cites work: Q5662096
cites work: Irreducible modules and parabolic subgroups
full work available at URL: https://doi.org/10.1007/bf01195017
OpenAlex ID: W1972078722
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description: scientific article; zbMATH DE number 3973163