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>
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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.
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