The Gelfand-Naimark-Segal construction for unitary representatins of Z2n\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

Classification of positive energy representations of the Virasoro group

We give a complete classification of all positive energy unitary representations of the Virasoro group. More precisely, we prove that every such representation can be expressed in an essentially unique way as a direct integral of irreducible highest weight representations