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# Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke Algebra, II

@inproceedings{Tanisaki2011KazhdanLusztigBA, title={Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke Algebra, II}, author={Toshiyuki Tanisaki and Nanhua Xi}, year={2011} }

- Published 2011
DOI:10.4171/JEMS/249

According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant Kgroup 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 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.