Mirabolic affine Grassmannian and character sheaves

Abstract

We compute the Frobenius trace functions of mirabolic character sheaves defined over a finite field. The answer is given in terms of the character values of general linear groups over the finite field, and the structure constants of multiplication in the mirabolic Hall-Littlewood basis of symmetric functions, introduced by Shoji.

v2: 22 pages. The final version published in Selecta Math. v3: Propositions 2 and 3 corrected

Cited by in corpus (1)

• On enhanced reductive groups (II): Finiteness of nilpotent orbits under enhanced group action and their closures