Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$

Cedric lecouvey

paper

Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$

arXiv:math/0211444

Abstract

We use Kashiwara's theory of crystal bases to study plactic monoids for $U_{q} (s o_{2 n + 1})$ and $U_{q} (s o_{2 n})$ . Simultaneously we describe a Schensted type correspondence in the crystal graphs of tensor powers of vector and spin representations and we derive a Jeu de Taquin for type $B$ from the Sheats sliding algorithm.

28 pages

Schensted-type correspondences and plactic monoids for types Bn​ and Dn​

Abstract

Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$