  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.
