Combinatorial Howe duality of symplectic type

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.