Kostant homology formulas for oscillator modules of Lie superalgebras

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• 作者：Shun-Jen Cheng ; Jae-Hoon Kwon ; Weiqiang Wang
• 关键词：Lie superalgebras ; Oscillator representations ; Howe duality ; Homology formulas
• 刊名：Advances in Mathematics
• 出版年：2010
• 出版时间：10 July 2010
• 年：2010
• 卷：224
• 期：4
• 页码：1548-1588
• 全文大小：415 K

文摘

We provide a systematic approach to obtain formulas for characters and Kostant -homology groups of the oscillator modules of the finite-dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite-dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highest weight representations of Hermitian symmetric pairs. In addition, two new reductive dual pairs related to the above-mentioned -homology computation are worked out.