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Remarks on the Schur-Howe-Sergeev Duality | | Shun-Jen Cheng
; Weiqiang Wang
; | | Date: |
15 Aug 2000 | | Journal: | Lett. Math. Phys. 52 (2000)143--153 | | Subject: | Representation Theory; Quantum Algebra | math.RT math.QA | | 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 $lambda$ 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. | | Source: | arXiv, math.RT/0008109 | | Services: | Forum | Review | PDF | Favorites | |
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