Dirac cohomology for graded affine Hecke algebras

Abstract

We define analogues of the Casimir and Dirac operators for graded affine Hecke algebras, and establish a version of Parthasarathy's Dirac operator inequality. We then prove a version of Vogan's Conjecture for Dirac cohomology. The formulation of the conjecture depends on a uniform geometric parametrization of spin representations of Weyl groups. Finally, we apply our results to the study of unitary representations.

22 pages

References in corpus (1)

• Functors for unitary representations of classical real groups and affine Hecke algebras

Cited by in corpus (2)

• Spin representations of Weyl groups and the Springer correspondence
• Dirac cohomology of one K-type representations