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.
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Communicated by: Yasuyuki Kawahigashi
The first author is supported by the Minerva foundation with funding from the Federal German Ministry for Education and Research.
The second author is partially supported by an NSF grant and by an ERC advanced grant.
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Gorelik, M., Kac, V.G., Möseneder Frajria, P. et al. Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs. Jpn. J. Math. 7, 41–134 (2012). https://doi.org/10.1007/s11537-012-1104-z
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DOI: https://doi.org/10.1007/s11537-012-1104-z