Kostant homology formulas for oscillator modules of Lie superalgebras

Details Kostant homology formulas for oscillator modules of Lie superalgebras Kostant homology formulas for oscillator modules of Lie superalgebras

2009-01-02

arxiv.org/abs/0901.0247v2

Advances in Mathematics 224 (2010), pp. 1548-1588

Mathematics

Representation Theory

Scientific paper

10.1016/j.aim.2010.01.002

We provide a systematic approach to obtain formulas for characters and Kostant ${\mathfrak u}$-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 ${\mathfrak u}$-homology computation are worked out.

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