Representations of Rank Two Affine Hecke Algebras

Abstract

This paper gives a complete analysis of the irreducible representations of affine Hecke algebras of rank two when the parameter q is not a root of unity. The irreducible representations are classified in terms of the Kazhdan-Lusztig classification and the relation to the Springer correspondence is given in detail. Each irreducible representation is constructed explicitly. These results are used in a crucial way in the classification of calibrated representations of general affine Hecke algebras as done in [Ra1] and [Ra4]. Though the same methods can be used to handle the very few root of unity cases (q2k = 1, k = 0, 1, 2, and also k = 3 in type A2, k = 4 in type B2 and k = 3,6 in type G2) wh..