Schensted-Type Correspondence, Plactic Monoid, and Jeu de Taquin for Type Cn

By C. Lecouvey. 2002

67 citations recorded by the source corpus.

We use Kashiwara's theory of crystal bases to study the plactic monoid for Uq(sp2n). Then we describe the corresponding insertion and sliding algorithms. The sliding algorithm is essentially the symplectic Jeu de Taquin defined by Sheats and our construction gives the proof of its compatibility with plactic relations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28860a7550d923dfb3de3be908c8939ce7392f55

Citations in the corpus

• Schensted-Type Correspondences and Plactic Monoids for Types Bn and Dn (2002, methodology): “This theorem is proved in the same way as in the symplectic case [ 10 ], and we will only sketch the arguments.”
• ON THE COMBINATORICS OF CRYSTAL GRAPHS, I. LUSZTIG'S INVOLUTION (2005, unknown): “As far as analogs of Schützenberger’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].”