Representations of graded hecke algebras

Abstract

Representations of affine and graded Hecke algebras associated to Weyl groups play an important role in the Langlands correspondence for the admissible representations of a reductive p-adic group. We work in the general setting of a graded Hecke algebra associated to any real reflection group with arbitrary parameters. In this setting we provide a classification of all irreducible representations of graded Hecke algebras associated to dihedral groups. Dimensions of generalized weight spaces, Langlands parameters, and a Springer-type correspondence are included in the classification. We also give an explicit construction of all irreducible calibrated representations (those possessing a simultane..