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

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

1999-10-18

arxiv.org/abs/math/9910086v1

Mathematics

Representation Theory

44 pages, latex

Scientific paper

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.

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