Remarks on the Schur–Howe–Sergeev Duality

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• 作者：Cheng ; Shun Jen ; Wang ; Weiqiang
• 关键词：Lie superalgebra q(n) ; Schur– ; Howe– ; Sergeev duality
• 刊名：Letters in Mathematical Physics
• 出版时间：2000
• 出版年：2000
• 期刊代码：33_03779017
• 类别：cp
• 卷：52
• 期：2
• 页码：143-153
• 数据来源：sp

摘要

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 $\backslash widetilde\; \{H\}\; \_k$ of the hyperoctahedral group H. 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 $\backslash widetilde\; \{H\}\; \_n$ parameterized by λ. We also discuss some consequences of this Howe duality.