English

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