Schensted-Type Correspondences and Plactic Monoids for Types Bn and Dn

By C. Lecouvey. 2002

52 citations recorded by the source corpus.

We use Kashiwara's theory of crystal bases to study plactic monoids for Uq(so2n+1) and Uq(so2n). 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4a6ffbd092692355f906ed1cc8ed1c309db7bc82

Citations in the corpus

• ON THE COMBINATORICS OF CRYSTAL GRAPHS, I. LUSZTIG'S INVOLUTION (2005, unknown): “on continuous arguments, is less transparent. As far as analogs of Schu¨tzenberger’s jeu de taquin are concerned, let us first mention the extensions to types Cn, Bn, and Dn due to Lecouvey and Sheats [19, 20, 32]. Let us also note that the only such analog known in the Littelmann path model is the o”