Abstract

We classify all triples $(G,V,H)$ such that $SL_n(q)\leq G\leq GL_n(q)$, $V$ is a representation of $G$ of dimension greater than one over an algebraically closed field ${\Bbb F}$ of characteristic prime to $q$, and $H$ is a proper subgroup of $G$ such that the restriction $V\downarrow_{H}$ is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.

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