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

Springer Science and Business Media LLC - Tập 181 - Trang 205-263 - 1996
Alain Lascoux1, Bernard Leclerc2, Jean-Yves Thibon3
1Institut Blaise Pascal L.I.T.P., Université Paris 7, Paris Cedex 05, France
2Université de Caen, Département de Mathématiques, Esplanade de la Paix, Caen Cedex, France
3Institut Gaspard Monge, Université de Marne-la-Vallée, Noisy-le-Grand Cedex, France

Tóm tắt

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 specializationq→1, our algorithm computes the decomposition matrices of all Hecke algebras at an th root of 1.

Tài liệu tham khảo

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