Combinatorial Howe duality of symplectic type

Abstract

We give a new combinatorial interpretation of Howe dual pairs of the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to this pair, in a uniform way which does not depend on $\g$. We introduce an analogue of jeu de taquin sliding for spinor model of irreducible characters of a Lie superalgebra $\g$ to define $P$-tableau and show that the associated $Q$-tableau is given by a symplectic tableau due to King.

38 pages

References in corpus (1)

• Flagged Littlewood-Richardson tableaux and branching rule for classical groups

Cited by in corpus (1)

• Skew Howe duality and limit shapes of Young diagrams