Remarks on the Schur-Howe-Sergeev duality

We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m),q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur-Sergeev duality between q(n) and a central extension (H) over tilde(k) of the hyperoctahedral group H. We show that the zero-weight space of a q(n)-module with highest weight lambda given by a strict partition of n is an irreducible module over the finite group (H) over tilde(n) parameterized by lambda. We also discuss some consequences of this Howe duality.