Differential Geometry
Geometric quantization for proper moment maps
[Quantification géométrique pour les applications moment propres]

Présenté par : Jean-Michel Bismut

Ma, Xiaonan1 ; Zhang, Weiping2
1 Université Denis-Diderot – Paris 7, UFR de mathématiques, case 7012, site Chevaleret, 75205 Paris cedex 13, France
2 Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 389-394.

Nous établissons une formule de quantification géométrique pour les actions hamiltoniennes d'un groupe de Lie compact agissant sur une variété symplectique non-compacte dont l'application moment est propre. En particulier, nous résolvons une conjecture formulée par Michèle Vergne dans son exposé à l'ICM 2006.

We establish a geometric quantization formula for Hamiltonian actions of a compact Lie group acting on a non-compact symplectic manifold such that the associated moment map is proper. In particular, we give a solution to a conjecture of Michèle Vergne.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.02.003
Ma, Xiaonan 1 ; Zhang, Weiping 2

1 Université Denis-Diderot – Paris 7, UFR de mathématiques, case 7012, site Chevaleret, 75205 Paris cedex 13, France
2 Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China 
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Ma, Xiaonan; Zhang, Weiping. Geometric quantization for proper moment maps. Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 389-394. doi : 10.1016/j.crma.2009.02.003. https://www.numdam.org/articles/10.1016/j.crma.2009.02.003/

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