Abstract
We show that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups. These sub super Lie groups are natural analogues of polarizing subgroups that appear in classical Kirillov theory. We obtain a concrete geometric parametrization of irreducible unitary representations by nonnegative definite coadjoint orbits. As an application, we prove an analytic generalization of the Stone-von Neumann theorem for Heisenberg-Clifford super Lie groups.
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Communicated by Y. Kawahigashi
This research is partially supported by an NSERC Discovery Grant.
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Salmasian, H. Unitary Representations of Nilpotent Super Lie Groups. Commun. Math. Phys. 297, 189–227 (2010). https://doi.org/10.1007/s00220-010-1035-6
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DOI: https://doi.org/10.1007/s00220-010-1035-6