Representations of the general linear groups which are irreducible over subgroups

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.