Geometric quantization for proper moment maps: the Vergne conjecture

TL;DR

This paper develops a geometric quantization formula for Hamiltonian group actions on noncompact symplectic manifolds with proper moment maps, advancing the understanding of quantization in noncompact settings.

Contribution

It provides a new geometric quantization formula specifically for noncompact symplectic manifolds with proper moment maps, addressing a key case in symplectic geometry.

Findings

Established a geometric quantization formula for noncompact manifolds

Extended the theory of moment maps to proper cases

Contributed to the proof of the Vergne conjecture

Abstract

We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.