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

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...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2013-08, Vol.217 (8), p.1427-1446
Main Authors: Magaard, Kay, Röhrle, Gerhard, Testerman, Donna M.
Format: Article
Language:English
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Summary: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⊗e and study its relationship to the maximal subgroup problem for finite classical groups.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2012.11.004