%0 Journal Article
%T Holomorphic Slices, Symplectic Reduction and Multiplicities of Representations
%A Reyer Sjamaar
%J Mathematics
%D 1993
%I arXiv
%X I prove the existence of slices for an action of a reductive complex Lie group on a K\"ahler manifold at certain orbits, namely those orbits that intersect the zero level set of a momentum map for the action of a compact real form of the group. I give applications of this result to symplectic reduction and geometric quantization at singular levels of the momentum map. In particular, I obtain a formula for the multiplicities of the irreducible representations occurring in the quantization in terms of symplectic invariants of reduced spaces, generalizing a result of Guillemin and Sternberg.
%U http://arxiv.org/abs/alg-geom/9304004v1