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

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

2002-11-28

arxiv.org/abs/math/0211444v1

Mathematics

Combinatorics

28 pages

Scientific paper

We use Kashiwara's theory of crystal bases to study plactic monoids for
$U_{q}(so_{2n+1})$ and $U_{q}(so_{2n})$. 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.

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