Holomorphic Slices, Symplectic Reduction and Multiplicities of Representations. Sjamaar, R. *arXiv:alg-geom/9304004*, April, 1993. arXiv: alg-geom/9304004Paper abstract bibtex I prove the existence of slices for an action of a reductive complex Lie group on a K\textbackslash"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.

@article{sjamaar_holomorphic_1993,
title = {Holomorphic {Slices}, {Symplectic} {Reduction} and {Multiplicities} of {Representations}},
url = {http://arxiv.org/abs/alg-geom/9304004},
abstract = {I prove the existence of slices for an action of a reductive complex Lie group on a K{\textbackslash}"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.},
urldate = {2019-09-10},
journal = {arXiv:alg-geom/9304004},
author = {Sjamaar, Reyer},
month = apr,
year = {1993},
note = {arXiv: alg-geom/9304004},
keywords = {Mathematics - Algebraic Geometry}
}

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