Dirac cohomology for graded affine Hecke algebras

• 成果类型: Article
• 署名作者: Barbasch, Dan; Ciubotaru, Dan; Trapa, Peter E.
• 署名单位: Cornell University; Utah System of Higher Education; University of Utah
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-012-0085-3
• 发表日期: 2012
• 页码: 197-227
• 关键词: unitary representations; conjecture; PROOF

摘要

We define an analogue of the Casimir element for a graded affine Hecke algebra , and then introduce an approximate square-root called the Dirac element. Using it, we define the Dirac cohomology H (D) (X) of an -module X, and show that H (D) (X) carries a representation of a canonical double cover of the Weyl group . Our main result shows that the -structure on the Dirac cohomology of an irreducible -module X determines the central character of X in a precise way. This can be interpreted as p-adic analogue of a conjecture of Vogan for Harish-Chandra modules. We also apply our results to the study of unitary representations of .