In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.
@article{bwmeta1.element.doi-10_2478_s11533-006-0019-4,
author = {Tomasz Przebinda},
title = {Local geometry of orbits for an ordinary classical lie supergroup},
journal = {Open Mathematics},
volume = {4},
year = {2006},
pages = {449-506},
zbl = {1141.17002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0019-4}
}
Tomasz Przebinda. Local geometry of orbits for an ordinary classical lie supergroup. Open Mathematics, Tome 4 (2006) pp. 449-506. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0019-4/
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