Characters of Springer representations on elliptic conjugacy classes

Abstract

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid again on elliptic conjugacy classes) of the W-character of an irreducible discrete series representation with real central character of a graded affine Hecke algebra with arbitrary parameters. In both cases, the Pin double cover of W and the Dirac operator for graded affine Hecke algebras play key roles.

15 pages, minor changes in exposition, corrected typos

References in corpus (1)

• Algebraic and analytic Dirac induction for graded affine Hecke algebras

Cited by in corpus (11)

• Algebraic and analytic Dirac induction for graded affine Hecke algebras
• Duality for Ext-groups and extensions of discrete series for graded Hecke algebras
• A uniform classification of discrete series representations of affine Hecke algebras
• Formal degrees of unipotent discrete series representations and the exotic Fourier transform
• Dirac Index and Twisted Characters
• Dirac cohomology for symplectic reflection algebras
• Dirac cohomology and simple modules of the Dunkl-Opdam subalgebra via inherited Drinfeld properties
• A Casselman-Osborne theorem for rational Cherednik algebras
• Dirac cohomology, elliptic representations and endoscopy
• Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index
• Dirac induction for rational Cherednik algebras