Relevement geometrique de la base canonique et involution de Schützenberger

Sophie Morier-Genoud

paper

Relevement geometrique de la base canonique et involution de Schützenberger

arXiv:math/0309424

Abstract

Let $G$ be a complex simply connected semisimple Lie group, and let $B_{V}$ be the canonical base of a Weyl module $V$ of $G$ . We calculate explicitely the action of the longest element $w_{0}$ of the Weyl group on $B_{V}$ in terms of parametrizations. The method is based on results of Berenstein and Zelevinsky on the geometric lifting.

5 pages, in French