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Irreducible geometric subgroups of classical algebraic groups


About this Title

Timothy C. Burness, Soumaïa Ghandour and Donna M. Testerman

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 239, Number 1130
ISBNs: 978-1-4704-1494-8 (print); 978-1-4704-2743-6 (online)
DOI: http://dx.doi.org/10.1090/memo/1130
Published electronically: June 9, 2015
Keywords:Classical algebraic group; disconnected maximal subgroup; irreducible triple

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Preliminaries
  • Chapter 3. The $\C _1, \C _3$ and $\C _6$ collections
  • Chapter 4. Imprimitive subgroups
  • Chapter 5. Tensor product subgroups, I
  • Chapter 6. Tensor product subgroups, II

Abstract


Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p ≥0$ 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 the triples $(G,H,V)$ of this form, where $H$ is a disconnected maximal positive-dimensional closed subgroup of $G$ preserving a natural geometric structure on $W$.

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