# Analytic R-groups of affine Hecke algebras - Mathematics > Representation Theory

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

Author: Eric Opdam, Patrick Delorme

Source: https://arxiv.org/