Generalized Loop Groups of Complex Manifolds, Gaussian Quasi-Invariant Measures on them and their Representations

Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are constructed. These measures are used for the studying of irreducible representations of such groups.