Dirac cohomology of one-W-type representations

Journal article

The smooth hermitian representations of a split reductive p-adic group whose restriction to a maximal hyperspecial compact subgroup contain a single K-type with Iwahori fixed vectors have been studied in [D. Barbasch, A. Moy, Classification of one K-type representations, Trans. Amer. Math. Soc. 351 (1999), no. 10, 4245-4261] in the more general setting of modules for graded affine Hecke algebras with parameters. We show that every such one K-type module has nonzero Dirac cohomology (in the sense of [D. Barbasch, D. Ciubotaru, P. Trapa, The Dirac operator for graded affine Hecke algebras, arXiv:1006.3822]), and use Dirac operator techniques to determine the semisimple part of the Langlands parameter for these modules, thus completing their classification.

Authors: Ciubotaru, D; Moy, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Mathematical Society
• Journal: Proceedings of the American Mathematical Society
• Volume: 143
• Issue: 3
• Pages: 1001-1013
• Publication date: 2014-01-01
• DOI: 10.1090/S0002-9939-2014-12303-3
• EISSN: 1088-6826
• ISSN: 0002-9939
• Keywords: group theory and generalizations; representations of Lie and linear algebraic groups over local fields; Hecke algebras and their representations