K(Fq)-invariants in Irreducible Representations of G(Fq), when G=GL_n


Anthony Henderson


Research Report 2001-5
Date: 24 July 2001


Using a general result of Lusztig, we give explicit formulas for the dimensions of K^F-invariants in irreducible representations of G^F, when G=GLn, F:G->G is a Frobenius map, and K is an F-stable subgroup of finite index in the fixed-point subgroup of an involution of G commuting with F. The proofs use some combinatorial facts about characters of symmetric groups.

Key phrases

representation. character. finite general linear group.

AMS Subject Classification (1991)

Primary: 20G40
Secondary: 20C15


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