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.
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