Geometric quantization for proper moment maps: the Vergne conjecture |
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| Authors: | Xiaonan Ma Weiping Zhang |
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| Affiliation: | 1. Institut de Mathématiques de Jussieu, Université Paris Diderot – Paris 7, UFR de Mathématiques, Case 7012, FR-75205, Paris Cedex 13, France
2. Chern Institute of Mathematics& LPMC, Nankai University, Tianjin, 300071, People’s Republic of China
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| 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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