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arXiv:0909.1227 [math.RT]AbstractReferencesReviewsResources

Analytic R-groups of affine Hecke algebras

Eric Opdam, Patrick Delorme

Published 2009-09-07, updated 2010-08-30Version 2

We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex group algebra of the $R$-group, twisted by a certain 2-cocycle $\gamma$. For classical Hecke algebras we prove that $\gamma$ is always trivial.

Comments: Some improvements in the presentation were made, and an example has been added showing the nontriviality of the cohomology class of the 2-cocycle $\gamma_\Delta$ (as opposed to $\gamma$ itself) for Hecke algebras of type D
Categories: math.RT
Subjects: 20C08, 22D25, 22E35, 43A40
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