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International Mathematics Research Notices (2004) 2004:31-53 , doi:10.1155/S1073792804131437
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Copyright © 2004 Hindawi Publishing Corporation. All rights reserved.

Analogue of Kostant's u-cohomology formula for the general linear superalgebra

Shun-Jen Cheng and R. B. Zhang

We determine in an explicit form the Lie superalgebra cohomology groups of the upper triangular odd subalgebra Formula of the general linear superalgebra Formula with coefficients in irreducible tensor modules over Formula. Using this, we develop a Weyl-type character formula for the irreducible tensor representations. Both in the computation of the cohomology groups and in the construction of the character formula, the Weyl group of the infinite-rank affine Kac-Moody algebra of A-type plays an essential role.


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 Int Math Res NoticesHome page
S.-J. Cheng and J.-H. Kwon
Howe Duality and Kostant Homology Formula for Infinite-Dimensional Lie Superalgebras
Int Math Res Notices, January 1, 2008; 2008(rnn085): rnn085 - 52.
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