R\'eflexions dans un cristal
Representation Theory
2012-10-25 v1 Quantum Algebra
Abstract
Let g = n^- + h + n^+ be a symmetrizable Kac-Moody algebra. Let B(\infty) 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 B(\infty) \otimes T_\lambda be the crystal of the integrable representation of highest weight \lambda. We compute the descending string parameters of an element b \otimes t_\lambda in B(\lambda) in terms of the Lusztig parameters of b.
Cite
@article{arxiv.1210.6464,
title = {R\'eflexions dans un cristal},
author = {Pierre Baumann and Stéphane Gaussent and Joel Kamnitzer},
journal= {arXiv preprint arXiv:1210.6464},
year = {2012}
}
Comments
4 pages; in French