Analytic R-groups of affine Hecke algebras

Abstract

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.

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

References in corpus (1)

• Opérateurs d'entrelacement et algèbres de Hecke avec paramètres d'un groupe réductif $p$-adique - le cas des groupes classiques

Cited by in corpus (4)

• On the classification of irreducible representations of affine Hecke algebras with unequal parameters
• Parabolically induced representations of graded Hecke algebras
• Extensions of tempered representations
• On characters and formal degrees of discrete series of affine Hecke algebras of classical types