Kostant Homology Formulas for Oscillator Modules of Lie Superalgebras
نویسنده
چکیده
We provide a systematic approach to obtain formulas for characters and Kostant u-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 u-homology computation are worked out.
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تاریخ انتشار 2009