The Gelfand-Naimark-Segal construction for unitary representatins of $\mathbb Z_2^n$-graded Lie supergroups

Abstract

We establish a Gelfand-Naimark-Segal construction which yields a correspondence between cyclic unitary representations and positive definite superfunctions of a general class of $\mathbb Z_2^n$-graded Lie supergroups.