Unitary representations of super groups and Mackey theory

We outline some basic facts in the theory of unitary representations of super Lie groups along the lines of [C. Carmeli, G. Cassinelli, A. Toigo, and V.S. Varadarajan. "Unitary representations of super lie groups and applications to the classification and multiplet structure of super particles", Comm. Math. Phys. 263 (2006) 217-258]. We define the concept of representation induced from a special sub super group. We give a version of Mackey theory for groups containing a special normal abelian connected sub super group.