Representations of the general linear groups which are irreducible over subgroups

Alexander S. Kleshchev; Pham Huu Tiep

Representations of the general linear groups which are irreducible over subgroups

Representation Theory 2008-11-18 v1 Group Theory

Authors: Alexander S. Kleshchev , Pham Huu Tiep

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 $\FF$ 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.

Keywords

representation theory of groups group representations representation theory of algebras

Cite

@article{arxiv.0811.2766,
  title  = {Representations of the general linear groups which are irreducible over subgroups},
  author = {Alexander S. Kleshchev and Pham Huu Tiep},
  journal= {arXiv preprint arXiv:0811.2766},
  year   = {2008}
}

Comments

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

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