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

S. V. Ludkovsky

paper

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

arXiv:math/9910086

Abstract

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 $μ$ on G relative to dense subgroups $G^{'}$ are constructed. These measures are used for the studying of irreducible representations of such groups.

44 pages, latex