Dirac cohomology for graded affine Hecke algebras

Author: 

Barbasch, D
Ciubotaru, D
Trapa, P

Publication Date: 

December 2012

Journal: 

ACTA MATHEMATICA

Last Updated: 

2020-09-10T09:18:22.84+01:00

Issue: 

2

Volume: 

209

DOI: 

10.1007/s11511-012-0085-3

page: 

197-227

abstract: 

We define an analogue of the Casimir element for a graded affine Hecke algebra H, and then introduce an approximate square-root called the Dirac element. Using it, we define the Dirac cohomology HD(X) of an,-module X, and show that HD(X) carries a representation of a canonical double cover of the Weyl group,. Our main result shows that the, -structure on the Dirac cohomology of an irreducible, -module X determines the central character of X in a precise way. This can be interpreted as p-adic analogue of a conjecture of Vogan for Harish-Chandra modules. We also apply our results to the study of unitary representations of,. © 2012 Institut Mittag-Leffler.

Symplectic id: 

511181

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article