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2014 Geometric quantization for proper moment maps: the Vergne conjecture
Xiaonan Ma, Weiping Zhang
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Acta Math. 212(1): 11-57 (2014). DOI: 10.1007/s11511-014-0108-3


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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Xiaonan Ma. Weiping Zhang. "Geometric quantization for proper moment maps: the Vergne conjecture." Acta Math. 212 (1) 11 - 57, 2014.


Received: 25 June 2012; Published: 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1380.53102
MathSciNet: MR3179607
Digital Object Identifier: 10.1007/s11511-014-0108-3

Rights: 2014 © Institut Mittag-Leffler

Vol.212 • No. 1 • 2014
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