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Kazhdan-Lusztig Basis and a Geometric Filtration of an Affine Hecke Algebra

Published online by Cambridge University Press:  11 January 2016

Toshiyuki Tanisaki  and
Nanhua Xi
Toshiyuki Tanisaki
Affiliation:
Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan, [email protected]
Nanhua Xi
Affiliation:
Institute of Mathematics, Chinese Academy of Sciences, Beijing, 100080, China, [email protected]
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Abstract

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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 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.

Keywords

20G0518F2520C08
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 182: Special Issue Celebrating the 60th Birthday of George Lusztig , June 2006 , pp. 285 - 311
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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