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Geometric quantization for proper moment maps: the Vergne conjecture

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Acta Mathematica

Abstract

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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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Paris Diderot – Paris 7, UFR de Mathématiques, Case 7012, FR-75205, Paris Cedex 13, France

    Xiaonan Ma

  2. Chern Institute of Mathematics& LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Weiping Zhang

Authors
  1. Xiaonan Ma
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  2. Weiping Zhang
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Correspondence to Xiaonan Ma.

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Ma, X., Zhang, W. Geometric quantization for proper moment maps: the Vergne conjecture. Acta Math 212, 11–57 (2014). https://doi.org/10.1007/s11511-014-0108-3

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  • DOI: https://doi.org/10.1007/s11511-014-0108-3

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