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 $\ge 1$, 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.

In the second version some typos were fixed and a paragraph about Hecke algebras of type B_n/C_n was added

Cited by in corpus (4)

• On principal series representations of quasi-split reductive p-adic groups
• Hochschild homology of twisted crossed products and twisted graded Hecke algebras
• Iwahori Matsumoto presentation for modules of Iwahori fixed functions on symmetric spaces
• Hermitian duals and generic representations for affine Hecke algebras