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

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

2008-06-16

arxiv.org/abs/0806.2480v1

International Mathematics Research Notices (2008) vol. 2008, article ID rnn085, 52 pages

Mathematics

Representation Theory

Scientific paper

10.1093/imrn/rnn085

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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