Kostant homology formulas for oscillator modules of Lie superalgebras

Abstract

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.

References in corpus (1)

• Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras

Cited by in corpus (14)

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• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• Irreducible Characters of Kac-Moody Lie superalgebras
• Infinite rank spinor and oscillator representations
• Higher level $q$-oscillator representations for $U_q(C_n^{(1)}),U_q(C^{(2)}(n+1))$ and $U_q(B^{(1)}(0,n))$
• Combinatorial Howe duality of symplectic type
• Dualities for Lie superalgebras
• Representations of the Lie Superalgebra $\mathfrak{osp}(1|2n)$ with Polynomial Bases
• Supercentralizers for deformations of the Pin osp dual pair
• Bernstein-Gelfand-Gelfand resolutions for linear superalgebras
• Littlewood identity and Crystal bases
• Super duality and homology of unitarizable modules of Lie algebras