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

References in corpus (3)

• Orbit closures in the enhanced nilpotent cone
• Quiver varieties and Beilinson-Drinfeld Grassmannians of type A
• Cherednik algebras for algebraic curves

Cited by in corpus (11)

• Orbit closures in the enhanced nilpotent cone
• An exotic Deligne-Langlands correspondence for symplectic groups
• The exotic Robinson-Schensted correspondence
• Orthosymplectic Satake equivalence
• Mirabolic Satake equivalence and supergroups
• Quiver Hall-Littlewood functions and Kostka-Shoji polynomials
• Modular generalized Springer correspondence: an overview
• Normality of orbit closures in the enhanced nilpotent cone
• Real double flag varieties for the symplectic group
• Enhanced adjoint action and their orbits for the general linear group
• On enhanced reductive groups (II): Finiteness of nilpotent orbits under enhanced group action and their closures