The Gelfand-Naimark-Segal construction for unitary representatins of ${\mathbb{Z}}_2^n$-graded Lie supergroups

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.