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.
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@article{CRMATH_2009__347_7-8_389_0, author = {Ma, Xiaonan and Zhang, Weiping}, 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}, url = {https://www.numdam.org/articles/10.1016/j.crma.2009.02.003/} }
TY - JOUR AU - Ma, Xiaonan AU - Zhang, Weiping TI - Geometric quantization for proper moment maps JO - Comptes Rendus. Mathématique PY - 2009 SP - 389 EP - 394 VL - 347 IS - 7-8 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2009.02.003/ DO - 10.1016/j.crma.2009.02.003 LA - en ID - CRMATH_2009__347_7-8_389_0 ER -
%0 Journal Article %A Ma, Xiaonan %A Zhang, Weiping %T Geometric quantization for proper moment maps %J Comptes Rendus. Mathématique %D 2009 %P 389-394 %V 347 %N 7-8 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2009.02.003/ %R 10.1016/j.crma.2009.02.003 %G en %F CRMATH_2009__347_7-8_389_0
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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