On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groups
Copyright policy )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 $p\ne {\rm char}(k)$ 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 $W^{\otimes e}$ and study its relationship to the maximal subgroup problem for finite classical groups.
To appear in Journal of Pure and Applied Algebra
- University of Birmingham United Kingdom
- École Polytechnique Fédérale de Lausanne EPFL Switzerland
- Ruhr University Bochum Germany
- hsg Bochum - University of Applied Sciences Germany
Representation theory for linear algebraic groups, Representations of finite groups of Lie type, Group Theory (math.GR), reducibility, maximal subgroups of classical groups, Linear algebraic groups over finite fields, Maximal subgroups, FOS: Mathematics, irreducible modules, quasisimple groups of Lie type, Mathematics - Group Theory, Group rings of finite groups and their modules (group-theoretic aspects)
Representation theory for linear algebraic groups, Representations of finite groups of Lie type, Group Theory (math.GR), reducibility, maximal subgroups of classical groups, Linear algebraic groups over finite fields, Maximal subgroups, FOS: Mathematics, irreducible modules, quasisimple groups of Lie type, Mathematics - Group Theory, Group rings of finite groups and their modules (group-theoretic aspects)
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