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

2012/01/10 by Magaard, Kay, Roehrle, Gerhard, Testerman, Donna
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1201.2057

Abstract

Let W be a vector space over an algebraically closed field k. Let H be a quasisimple group of Lie type of characteristic p≠ \rm 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.

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