Representations of the general linear groups which are irreducible over subgroups

2008/11/17 by Alexander S. Kleshchev, Kleshchev, Alexander S., Pham Huu Tiep +1
Mathematics · #20C20 #20E28 #20G40 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C20 #msc:20E28 #msc:20G40

paper · pdf · doi:10.48550/arxiv.0811.2766

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

arxiv created 2008/11/17 · arxiv updated 2009/12/01

Abstract

We classify all triples (G,V,H) such that SL_n(q)≤ G≤ 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.

Related

• Representations of finite special linear groups in non-defining characteristic
• Irreducible restrictions of representations of symmetric and alternating\n groups in small characteristics
• Cross-Characteristic Representations of Sp₆(2^a) and Their Restrictions to Maximal Subgroups
• Representations of GL_n(D) near the identity
• Irreducible subgroups of simple algebraic groups - a survey