Dirac cohomology for graded affine Hecke algebras
Representation Theory
2010-06-22 v1
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.
Keywords
Cite
@article{arxiv.1006.3822,
title = {Dirac cohomology for graded affine Hecke algebras},
author = {Dan Barbasch and Dan Ciubotaru and Peter E. Trapa},
journal= {arXiv preprint arXiv:1006.3822},
year = {2010}
}
Comments
22 pages