Holomorphic Slices, Symplectic Reduction and Multiplicities of Representations

1993/04/12 by Sjamaar, Reyer · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9304004

Abstract

I prove the existence of slices for an action of a reductive complex Lie group on a Kähler 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.

Cited by

• Slices for reductive group actions in algebraic and holomorphic symplectic geometry
• Quantization commutes with reduction for coisotropic A-branes
• A structure theorem along fibers of extreme points of the momentum polytope

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