Schensted-type correspondences and plactic monoids for types Bn and Dn
نویسنده
چکیده
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.
منابع مشابه
Schensted-Type Correspondences and Plactic Monoids for Types <Emphasis Type="Italic">B</Emphasis><Subscript>n</Subscript> and <Emphasis Type="Italic">D</Emphasis><Subscript>n</Subscript>
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.
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This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types An, Bn, Cn, Dn, and G2, using a unified proof strategy that depends on Kashiwara’s crystal bases and analogies of Young tableaux, and on Lecouvey’s presentations for these monoids. As corollaries, we deduce that Plactic monoids of these types have finite derivation type and satisfy the homolog...
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