Acta Mathematica

Geometric quantization for proper moment maps: the Vergne conjecture

Xiaonan Ma and Weiping Zhang

Full-text: Open access

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.

Article information

Source
Acta Math., Volume 212, Number 1 (2014), 11-57.

Dates
Received: 25 June 2012
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485801725

Digital Object Identifier
doi:10.1007/s11511-014-0108-3

Mathematical Reviews number (MathSciNet)
MR3179607

Zentralblatt MATH identifier
1380.53102

Rights
2014 © Institut Mittag-Leffler

Citation

Ma, Xiaonan; Zhang, Weiping. Geometric quantization for proper moment maps: the Vergne conjecture. Acta Math. 212 (2014), no. 1, 11--57. doi:10.1007/s11511-014-0108-3. https://projecteuclid.org/euclid.acta/1485801725


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