Irreducible subgroups of simple algebraic groups - a survey

Tim Burness, Donna Testerman

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Abstract

Let G be a simple linear algebraic group over an algebraically closed field K of characteristic p > 0, let H be a proper closed subgroup of G and let V be a nontrivial finite dimensional irreducible rational KG-module. We say that (G, H, V ) is an irreducible triple if V is irreducible as a KH-module. Determining these triples is a fundamental problem in the representation theory of algebraic groups, which arises naturally in the study of the subgroup structure of classical groups. In the 1980s, Seitz and Testerman extended earlier work of Dynkin on connected subgroups in characteristic zero to all algebraically closed fields. In this article we will survey recent advances towards a classification of irreducible triples for all positive dimensional subgroups of simple algebraic groups.
Original languageEnglish
Title of host publicationGroups St Andrews 2017 in Birmingham
PublisherCambridge University Press
Chapter9
Pages230-260
Number of pages32
ISBN (Print)9781108728744
Publication statusPublished - 1 Apr 2019

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
ISSN (Print)0076-0552

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