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

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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/