Analytic R-groups of affine Hecke algebras
Representation Theory
2010-09-01 v2
Abstract
We define analytic -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 -group, twisted by a certain 2-cocycle . For classical Hecke algebras we prove that is always trivial.
Keywords
Cite
@article{arxiv.0909.1227,
title = {Analytic R-groups of affine Hecke algebras},
author = {Eric Opdam and Patrick Delorme},
journal= {arXiv preprint arXiv:0909.1227},
year = {2010}
}
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