On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groups

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Let W be a vector space over an algebraically closed field k. Let H be a quasisimple group of Lie type of characteristic p≠char(k) acting irreducibly on W. Suppose also that G is a classical group with natural module W, chosen minimally with respect to containing the image of H under the associated representation. We consider the question of when H can act irreducibly on a G-constituent of W and study its relationship to the maximal subgroup problem for finite classical groups.


Original languageEnglish
Pages (from-to)1427-1446
Number of pages20
JournalJournal of Pure and Applied Algebra
Issue number8
Early online date4 Jan 2013
Publication statusPublished - 1 Aug 2013