2010/06/18 by Barbasch, Dan, Ciubotaru, Dan, Trapa, Peter E.
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1006.3822
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.