%0 Journal Article
%T Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra
%A Toshiyuki Tanisaki
%A Nanhua Xi
%J Mathematics
%D 2004
%I arXiv
%X According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant $K$-group of Steinberg's triple variety. The $K$-group is equipped with a filtration indexed by closed $G$-stable subvarieties of the nilpotent variety, where $G$ is the corresponding reductive algebraic group over $\mathbb{C}$. In this paper we will show in the case of type $A$ that the filtration is compatible with the Kazhdan-Lusztig basis of the Hecke algebra.
%U http://arxiv.org/abs/math/0411304v1