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

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

2012-01-10

arxiv.org/abs/1201.2057v1

Mathematics

Group Theory

Scientific paper

Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting irreducibly on $W$. Suppose that $G$ is a classical group with natural module $W$. Suppose also that $G$ is a classical group with natural module, 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 $W^{\otimes e}$ and study its relationship to the maximal subgroup problem for finite classical groups.

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