Schensted-Type correspondence, Plactic Monoid and Jeu de Taquin for type Cn
نویسنده
چکیده
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.
منابع مشابه
Schensted-type correspondences and plactic monoids for types Bn and Dn
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.
متن کاملSchensted-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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