From the same journal

From the same journal

Reductive pairs arising from representations

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JournalJournal of Algebra
DateE-pub ahead of print - 1 Mar 2016
DatePublished (current) - 1 Jun 2016
Volume455
Number of pages15
Pages (from-to)93-107
Early online date1/03/16
Original languageEnglish

Abstract

Let G be a reductive algebraic group and V a G-module. We consider the question of when (GL(V), ρ(G)) is a reductive pair of algebraic groups, where ρ is the representation afforded by V. We first make some observations about general G and V, then specialise to the group SL2(K) with K algebraically closed of positive characteristic p. For this group we provide complete answers for the classes of simple and Weyl modules, the behaviour being determined by the base p expansion of the highest weight of the module. We conclude by illustrating some of the results from the first section with examples for the group SL3(K).

    Research areas

  • Reductive pairs of algebraic groups, Representations of algebraic groups

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