Advanced Studies in Pure Mathematics

On tensor categories attached to cells in affine Weyl groups

Roman Bezrukavnikov

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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.

Article information

Source
Representation Theory of Algebraic Groups and Quantum Groups, T. Shoji, M. Kashiwara, N. Kawanaka, G. Lusztig and K. Shinoda, eds. (Tokyo: Mathematical Society of Japan, 2004), 69-90

Dates
Received: 13 February 2002
Revised: 12 November 2002
First available in Project Euclid: 3 January 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546542382

Digital Object Identifier
doi:10.2969/aspm/04010069

Mathematical Reviews number (MathSciNet)
MR2074589

Zentralblatt MATH identifier
1078.20044

Citation

Bezrukavnikov, Roman. On tensor categories attached to cells in affine Weyl groups. Representation Theory of Algebraic Groups and Quantum Groups, 69--90, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/04010069. https://projecteuclid.org/euclid.aspm/1546542382


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