Reflections in a crystal

Let g = n(-) circle plus h circle plus n(+) be a symmetrizable Kac-Moody algebra. Let B(infinity) be the Kashiwara crystal of U-q(n(-)), let lambda be a dominant integral weight, let T-lambda = {t(lambda)} be the crystal with one element of weight lambda. and let B(lambda) subset of B(infinity) circle times T-lambda be the crystal of the integrable representation of highest weight lambda. We compute the descending string parameters of an element b circle times t(lambda) in B(lambda) in terms of the Lusztig parameters of b. C) 2012 Publie par Elsevier Masson SAS pour l'Academie des sciences.