Hecke algebras and harmonic analysis on p-adic groups

Abstract. We compute Plancherel measures and formal degrees for unipotent representations of p-adic groups, using Hecke algebra isomorphisms. The results verify special cases of the conjectural uniformity of formal degrees in an L-packet. 1. Introduction. In this paper we compute some numerical quantities aris-ing from induced representations of reductive p-adic groups, namely Plancherel measures, formal degrees, and the ubiquitous constant called (G=P) by Harish-Chandra. All three are given by integrals which are difficult to evaluate directly. Here they are found with the aid of Hecke algebras, in the following situations