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arXiv · 0806.2480

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

Shun-Jen Cheng·Jae-Hoon Kwon
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Abstract

Using Howe duality we compute explicitly Kostant-type homology groups for a wide class of representations of the infinite-dimensional Lie superalgebra $\hat{\frak{gl}}_{\infty|\infty}$ and its classical subalgebras at positive integral levels. We also obtain Kostant-type homology formulas for the Lie algebra $ widehat{\frak{gl}}_\infty$ at negative integral levels. We further construct resolutions in terms of generalized Verma modules for these representations.

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BibTeXRIS

Shun-Jen Cheng, Jae-Hoon Kwon. 2008-06-16. Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras. https://doi.org/10.1093/imrn%2Frnn085

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