Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.
Schensted-type correspondences and plactic monoids for types $B_{n}$ and $D_{n}$
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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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2026 1verdicts
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Presentations for categories of crystals
Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.