Open Access
VOL. 40 | 2004 On tensor categories attached to cells in affine Weyl groups
Chapter Author(s) Roman Bezrukavnikov
Editor(s) Toshiaki Shoji, Masaki Kashiwara, Noriaki Kawanaka, George Lusztig, Ken-ichi Shinoda
Adv. Stud. Pure Math., 2004: 69-90 (2004) DOI: 10.2969/aspm/04010069

Abstract

This note is devoted to Lusztig's bijection between unipotent conjugacy classes in a simple complex algebraic group and 2-sided cells in the affine Weyl group of the Langlands dual group; and also to the description of the reductive quotient of the centralizer of the unipotent element in terms of convolution of perverse sheaves on affine flag variety of the dual group conjectured by Lusztig in [L4]. Our main tool is a recent construction by Gaitsgory (based on an idea of Beilinson and Kottwitz), the so-called sheaf-theoretic construction of the center of an affine Hecke algebra (see [Ga]). We show how this remarkable construction provides a geometric interpretation of the bijection, and allows to prove the conjecture.

Information

Published: 1 January 2004
First available in Project Euclid: 3 January 2019

zbMATH: 1078.20044
MathSciNet: MR2074589

Digital Object Identifier: 10.2969/aspm/04010069

Rights: Copyright © 2004 Mathematical Society of Japan

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