Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs
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Kac_Denominator identities.pdf
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Author(s)
Gorelik, Maria
Möseneder Frajria, Pierluigi
Papi, Paolo
Kac, Victor
Date Issued
March 2012
Journal
Japanese Journal of Mathematics
Publisher
Springer-Verlag
Citation
Gorelik, Maria, Victor G. Kac, Pierluigi Möseneder Frajria, and Paolo Papi. “Denominator Identities for Finite-Dimensional Lie Superalgebras and Howe Duality for Compact Dual Pairs.” Japanese Journal of Mathematics 7, no. 1 (March 2012): 41–134.
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Author's final manuscript
Abstract
We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups, and, as an application of these formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s11537-012-1104-z
