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arXiv · 1006.3822

Dirac cohomology for graded affine Hecke algebras

Dan Barbasch·Dan Ciubotaru·Peter E. Trapa
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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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BibTeXRIS

Dan Barbasch, Dan Ciubotaru, Peter E. Trapa. 2010-06-18. Dirac cohomology for graded affine Hecke algebras. https://arxiv.org/abs/1006.3822

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