论文信息 - A Simple Algorithm for Computing the Global Crystal Basis of an Irreducible Uq(sln)-Module

A Simple Algorithm for Computing the Global Crystal Basis of an Irreducible Uq(sln)-Module

We describe a simple algorithm for computing Kashiwara's global crystal basis of a finite-dimensional irreducible representation of Uq(sln). Resume: Nous decrivons un algorithme simple pour calculer la base cristalline globale de Kashiwara d'une representation irreductible de dimension finie de Uq(sln).

Philippe Toffin | Bernard Leclerc | B. Leclerc | Philippe Toffin

[1] D. Kazhdan,et al. Special bases forSN and GL(n) , 1981 .

[2] Israel M. Gelfand,et al. Finite-dimensional representations of the group of unimodular matrices , 1950 .

[3] Masaki Kashiwara,et al. Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras , 1994 .

[4] Alain Lascoux,et al. Hecke algebras at roots of unity and crystal bases of quantum affine algebras , 1996 .

[5] M. Kashiwara,et al. On crystal bases of the $Q$-analogue of universal enveloping algebras , 1991 .

[6] A. Pressley,et al. A guide to quantum groups , 1994 .

[7] J. Thibon,et al. q-Deformed Fock spaces and modular representations of spin symmetric groups , 1997, q-alg/9702001.

[8] A. Zelevinsky,et al. String bases for quantum groups of type ᵣ , 1993 .

[9] George Lusztig,et al. Canonical bases arising from quantized enveloping algebras , 1990 .

[10] R. Carter. LECTURES ON QUANTUM GROUPS (Graduate Studies in Mathematics 6) By Jens Carsten Jantzen: 266 pp., US$44.00, ISBN 0 8218 0478 2 (American Mathematical Society, 1996). , 1997 .