Comptes Rendus
no. 7-8
Differential Geometry
Geometric quantization for proper moment maps
[Quantification géométrique pour les applications moment propres]

Présenté par : Jean-Michel Bismut

Xiaonan Ma1 ; Weiping Zhang2
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, Volume 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
Xiaonan Ma 1 ; Weiping Zhang 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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Xiaonan Ma; Weiping Zhang. Geometric quantization for proper moment maps. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 389-394. doi : 10.1016/j.crma.2009.02.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.003/

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