A formula of Arthur and affine Hecke algebras

Abstract

Let $\pi ,{\pi }^{\prime }$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincaré pairing $EP(\pi ,{\pi }^{\prime })$, the alternating sum of the dimensions of the Ext-groups. We show that $EP(\pi ,{\pi }^{\prime })$ can be expressed in a simple formula involving an analytic R-group, analogous to a formula of Arthur in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over nonarchimedean local fields of arbitrary characteristic.

22 pages

References in corpus (1)

• Periodic cyclic homology of affine Hecke algebras