Irreducible geometric subgroups of classical algebraic groups

Tim C Burness, Soumaia Ghandour, Donna M Testerman

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Abstract

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable $p$-restricted rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper we classify all such triples $(G,H,V)$, where $H$ is a maximal closed disconnected positive-dimensional subgroup of $G$, and $H$ preserves a natural geometric structure on $W$.
Original languageEnglish
Article number1130
Number of pages100
JournalMemoirs of the American Mathematical Society
Volume239
Issue number1130
Early online date9 Jun 2015
DOIs
Publication statusPublished - 2016

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