Nagoya Mathematical Journal

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

Toshiyuki Tanisaki and 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.

Article information

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

Dates
First available in Project Euclid: 20 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1150810010

Mathematical Reviews number (MathSciNet)
MR2235345

Zentralblatt MATH identifier
1165.20003

Subjects
Primary: 20G05: Representation theory 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 20C08: Hecke algebras and their representations

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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