Affine Hecke algebras and their representations

Abstract

This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible representations. Only at the end we establish a new result: a natural bijection between the set of irreducible representations of an affine Hecke algebra with real parameters $\geq 1$, and the set of irreducible representations of the affine Weyl group underlying the algebra. This can be regarded as a generalized Springer correspondence with affine Hecke algebras.