On irreducible subgroups of simple algebraic groups

Tim C Burness, Claude Marion, Donna Testerman

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Abstract

Let G be a simple 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 irreducible KG-module, which is p-restricted, tensor indecomposable and rational. Assume that the restriction of V to H is irreducible. In this paper, we study the triples (G, H, V ) of this form when G is a classical group and H is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (G, H, V ) to the case where G is an orthogonal group, V is a spin module and H normalizes an orthogonal decomposition of the natural KG-module.
Original languageEnglish
Pages (from-to)1259-1309
Number of pages51
JournalMathematische Annalen
Volume367
Issue number3
Early online date11 Jun 2016
DOIs
Publication statusPublished - Apr 2017

Keywords

  • Primary 20G05
  • Secondary 20E28
  • 20E32

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