Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665253 | Advances in Mathematics | 2015 | 50 Pages |
Abstract
In this paper, we give a uniform construction of irreducible genuine characters of the Pin cover W˜ of a Weyl group W , and put them into the context of theory of Springer representations. In the process, we provide a direct connection between Springer theory, via Green polynomials, the irreducible representations of W˜, and an extended Dirac operator for graded Hecke algebras. We also introduce a q-elliptic pairing for W with respect to the reflection representation V. These constructions are of independent interest. The q-elliptic pairing is a generalization of the elliptic pairing of W introduced by Reeder, and it is also related to S. Kato's notion of (graded) Kostka systems for the semidirect product AW=C[W]⋉S(V)AW=C[W]⋉S(V).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Dan Ciubotaru, Xuhua He,