Geometric quantization for proper moment maps: the Vergne conjecture

Xiaonan Ma Institut de Mathématiques de Jussieu, Université Paris Diderot – Paris 7 Weiping Zhang Chern Institute of Mathematics& LPMC, Nankai University

Differential Geometry mathscidoc:1701.10005

Acta Mathematica, 212, (1), 11-57, 2012.6
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.
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@inproceedings{xiaonan2012geometric,
  title={Geometric quantization for proper moment maps: the Vergne conjecture},
  author={Xiaonan Ma, and Weiping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402307131784},
  booktitle={Acta Mathematica},
  volume={212},
  number={1},
  pages={11-57},
  year={2012},
}
Xiaonan Ma, and Weiping Zhang. Geometric quantization for proper moment maps: the Vergne conjecture. 2012. Vol. 212. In Acta Mathematica. pp.11-57. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402307131784.
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