## Nagoya Mathematical Journal

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

#### 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.

#### Article information

Source
Nagoya Math. J., Volume 182 (2006), 285-311.

Dates
First available in Project Euclid: 20 June 2006

https://projecteuclid.org/euclid.nmj/1150810010

Mathematical Reviews number (MathSciNet)
MR2235345

Zentralblatt MATH identifier
1165.20003

#### Citation

Tanisaki, Toshiyuki; Xi, Nanhua. Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra. Nagoya Math. J. 182 (2006), 285--311. https://projecteuclid.org/euclid.nmj/1150810010

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