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

## Author

**Anthony Henderson**

## Status

Research Report 2001-5

Date: 24 July 2001

## Abstract

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=GL*_{n},
*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

## Content

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