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Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra

Toshiyuki Tanisaki·Nanhua Xi
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Abstract

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.

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Toshiyuki Tanisaki, Nanhua Xi. 2004-11-13. Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra. https://arxiv.org/abs/math/0411304

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