Schensted-type correspondences and plactic monoids for types B_n and D_n

2002/11/28 by Cédric Lecouvey, Cedric lecouvey, lecouvey, Cedric
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.math/0211444

28 pages

arxiv created 2002/11/28 · arxiv updated 2009/11/30

Abstract

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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