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.
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.
Accepted:
Published online:
Xiaonan Ma 1; Weiping Zhang 2
@article{CRMATH_2009__347_7-8_389_0, author = {Xiaonan Ma and Weiping Zhang}, title = {Geometric quantization for proper moment maps}, journal = {Comptes Rendus. Math\'ematique}, pages = {389--394}, publisher = {Elsevier}, volume = {347}, number = {7-8}, year = {2009}, doi = {10.1016/j.crma.2009.02.003}, language = {en}, }
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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