Remarks on the Schur-Howe-Sergeev Duality

2000/08/15 by Shun-Jen Cheng, Weiqiang Wang · 1 citation
Mathematics · #math.RT #math.QA

paper · pdf

published as Lett. Math. Phys. 52 (2000)143--153 · 11 pages, to appear in Lett. Math. Phys

arxiv created 2000/08/15 · arxiv updated 2009/11/30

Abstract

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 λ given by a strict partition of n is an irreducible module over the finite group \Hy_n parameterized by λ. We also discuss some consequences of this Howe duality.

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