K(Fq)-invariants in Irreducible Representations of G(Fq), when G=GL_n
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.
representation. character. finite general linear group.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics