Réflexions dans un cristal

Abstract

Let g = n^- + h + n^+ be a symmetrizable Kac-Moody algebra. Let B(\infty) be the Kashiwara crystal of U_q(n^-), let λbe a dominant integral weight, let T_λ= {t_λ} be the crystal with one element of weight λ, and let B(λ) \subset B(\infty) \otimes T_λbe the crystal of the integrable representation of highest weight λ. We compute the descending string parameters of an element b \otimes t_λin B(λ) in terms of the Lusztig parameters of b.

4 pages; in French