%0 Journal Article
%T Analytic R-groups of affine Hecke algebras
%+ Institut de mathématiques de Luminy (IML)
%+ Korteweg-de Vries Institute for Mathematics
%A Delorme, Patrick
%A Opdam, Eric
%Z 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
%< avec comité de lecture
%@ 0075-4102
%J Journal für die reine und angewandte Mathematik
%I Walter de Gruyter
%V 2011
%N 658
%P 133-172
%8 2011-01
%D 2011
%Z 0909.1227
%R 10.1515/crelle.2011.064
%Z 20C08, 22D25, 22E35, 43A40
%Z Mathematics [math]/Representation Theory [math.RT]Journal articles
%X 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.
%G English
%L hal-01273294
%U https://hal.science/hal-01273294
%~ CNRS
%~ UNIV-AMU
%~ IML
%~ I2M
%~ ANR