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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn085, 52 pages, doi:10.1093/imrn/rnn085 published on August 7, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Howe Duality and Kostant Homology Formula for Infinite-Dimensional Lie Superalgebras

Shun-Jen Cheng1 and Jae-Hoon Kwon2

1 Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529
2 Department of Mathematics, University of Seoul, Seoul 130-743, Korea

Correspondence: Correspondence to be sent to: jhkwon{at}uos.ac.kr

Using Howe duality, we compute explicitly Kostant-type homology groups for a wide class of representations of the infinite-dimensional Lie superalgebra Formula and its classical subalgebras at positive integral levels. We also obtain Kostant-type homology formulas for the Lie algebra Formula at negative integral levels. We further construct resolutions in terms of generalized Verma modules for these representations.



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This Article
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