Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q}(G_{2})$-module

cedric Lecouvey

paper

Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q} (G_{2})$ -module

arXiv:math/0211443

Abstract

We use Kang-Misra's combinatorial description of the crystal graphs for $U_{q} (G_{2})$ to introduce the plactic monoid for type $G_{2}$ . Then we describe the corresponding insertion algorithm which yields a Schensted type correspondence. Next we give a simple algorithm for computing the canonical basis of any finite dimensional $U_{q} (G_{2})$ -module.

19 pages

Schensted type correspondence for type G2​ and computation of the canonical basis of a finite dimensional Uq​(G2​)-module

Abstract

Schensted type correspondence for type $G_{2}$ and computation of the canonical basis of a finite dimensional $U_{q} (G_{2})$ -module