Representations of the general linear groups which are irreducible over subgroups

Alexander S. Kleshchev; Pham Huu Tiep

paper

Representations of the general linear groups which are irreducible over subgroups

arXiv:0811.2766

Abstract

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

36 pages. Amer. J. Math., to appear