2010/11/02 by Opdam, Eric, Solleveld, Maarten
#20C08 #22E50 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1011.0679
Let π, π' be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincaré pairing EP (π,π'), the alternating sum of the dimensions of the Ext-groups. We show that EP (π,π') 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.