Unitary representations of nilpotent super Lie groups

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.

References in corpus (1)

• Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles

Cited by in corpus (10)

• Superorbits
• A minimal representation of the orthosymplectic Lie supergroup
• Noncommutative Supergeometry and Quantum Supergroups
• Fréchet globalisations of Harish-Chandra supermodules
• $Q$-representations and unitary representations of the super-Heisenberg group and harmonic superanalysis
• A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra $\mathfrak{osp}(m,2|2n)$
• $C^{\ast }$-algebras and direct integral decomposition for Lie supergroups
• A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha )$
• Unitary Harish-Chandra representations of real supergroups
• A coadjoint orbit-like construction for Jordan superalgebras