Analytic R-groups of affine Hecke algebras

Details Analytic R-groups of affine Hecke algebras Analytic R-groups of affine Hecke algebras

2009-09-07

arxiv.org/abs/0909.1227v2

Mathematics

Representation Theory

Some improvements in the presentation were made, and an example has been added showing the nontriviality of the cohomology cla

Scientific paper

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.

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