Hecke algebras at roots of unity and crystal bases of quantum affine algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Hecke algebras at roots of unity and crystal bases of quantum affine algebras

Authors:	Alain Lascoux Bernard Leclerc Jean-Yves Thibon

Institution:	(1) Institut Blaise Pascal L.I.T.P., Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France;(2) Université de Caen, Département de Mathématiques, Esplanade de la Paix, BP 5186, 14032 Caen Cedex, France;(3) Institut Gaspard Monge, Université de Marne-la-Vallée, 2 rue de la Butte-Verte, 93166 Noisy-le-Grand Cedex, France

Abstract:	We present a fast algorithm for computing the global crystal basis of the basic $U_q (\widehat{\mathfrak{s}\mathfrak{l}}_n )$ -module. This algorithm is based on combinatorial techniques which have been developed for dealing with modular representations of symmetric groups, and more generally with representations of Hecke algebras of typeA at roots of unity. We conjecture that, upon specializationq1, our algorithm computes the decomposition matrices of all Hecke algebras at an ^th root of 1.Partially supported by PRC Math-Info and EEC grant n⁰ ERBCHRXCT930400.

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