Unitary Representations of Nilpotent Super Lie Groups

We prove that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups which are natural generalizations of polarizing subgroups that appear in classical Kirillov theory. We prove that this kind of induction always yields irreducible unitary representations. We also prove a uniqueness result for the inducing data, and as a corollary we obtain a simple integervalued invariant of irreducible unitary representations. Along the way, we obtain a proof of an analytic generalization of the Stone-von Neumann theorem for Heisenberg-Clifford super Lie groups.