关键词: representation, affine Hecke algebra, affine Weyl groups, Hecke algebra

Abstract:

Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use H_q to denote an affine Hecke algebra over k of type G₂ with parameter q. The purpose of this paper is to study representations of H_q  by using based rings of two-sided cells of an affine Weyl group W of type G₂. We shall give the classification of irreducible representations of H_q. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known  to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between H_q and an Hecke algebra corresponding to a certain Coxeter group. Apparently  the idea in this paper works for all affine Weyl groups, but that is the theme of another paper.

Key words: representation, affine Hecke algebra, affine Weyl groups, Hecke algebra