Kᶠ-invariants in irreducible representations of Gᶠ, when G=GLₙ

الأصل · EN

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