Remarks on the Schur-Howe-Sergeev Duality

Details Remarks on the Schur-Howe-Sergeev Duality Remarks on the Schur-Howe-Sergeev Duality

2000-08-15

arxiv.org/abs/math/0008109v1

Lett. Math. Phys. 52 (2000)143--153

Mathematics

Representation Theory

11 pages, to appear in Lett. Math. Phys

Scientific paper

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 $\Hy_k$ of the hyperoctahedral group H_k. 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 $\Hy_n$ parameterized by $\lambda$. We also discuss some consequences of this Howe duality.

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