Geometric quantization for proper moment maps: the Vergne conjecture

By Xiaonan Ma, Weiping Zhang. 2008

74 citations recorded by the source corpus.

We establish an analytic interpretation for the index of certain transversally elliptic symbols on non-compact manifolds. By using this interpretation, we establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a non-compact symplectic manifold with proper moment map. In particular, we present a solution to a conjecture of Michèle Vergne in her ICM 2006 plenary lecture.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b660229f6491733d6029f49d12b56b2a6023a2a