Poisson Measures for Topological Groups and Their Representations

A class of unitary strongly continuous representations of infinite-dimensional groups such as geometric loop and diffeomorphism groups of real, complex and non-Archimedean manifolds is investigated. This class is constructed by producing Poisson measures P_m on configuration spaces of infinite-dimensional topological groups with the help of quasi-invariant measures m. Their irreducibility, equivalence and inequivalence is investigated.