Discrete series characters for affine Hecke algebras and their formal degrees

Abstract

We introduce the generic central character of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine Hecke algebras (except for the types ${E_{n}^{(1)}}$ , n=6, 7, 8) with arbitrary positive parameters and we prove an explicit product formula for their formal degrees (in all cases).