Let be a compact Lie group acting in a Hamiltonian way on a symplectic manifold which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map is proper so that the reduced space is compact for all . Then, we can define the “formal geometric quantization” of as
The aim of this article is to study the functorial properties of the assignment .
Considérons l’action hamiltonienne d’un groupe de Lie compact sur une variété symplectique préquantifiée par un fibré en droites de Kostant-Souriau. On suppose que l’application moment est propre, ainsi les réductions symplectiques sont compactes pour tout . On peut alors définir la quantification formelle de comme
Le but de ce travail est l’étude de certaines propriétés fonctorielles de l’application .
Keywords: Geometric quantization, moment map, symplectic reduction, index, transversally elliptic
Mot clés : quantification géométrique, application moment, réduction symplectique, indice, transversalement elliptique
@article{AIF_2009__59_1_199_0, author = {Paradan, Paul-\'Emile}, title = {Formal geometric quantization}, journal = {Annales de l'Institut Fourier}, pages = {199--238}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {1}, year = {2009}, doi = {10.5802/aif.2429}, zbl = {1163.53056}, mrnumber = {2514864}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2429/} }
TY - JOUR AU - Paradan, Paul-Émile TI - Formal geometric quantization JO - Annales de l'Institut Fourier PY - 2009 SP - 199 EP - 238 VL - 59 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2429/ DO - 10.5802/aif.2429 LA - en ID - AIF_2009__59_1_199_0 ER -
Paradan, Paul-Émile. Formal geometric quantization. Annales de l'Institut Fourier, Volume 59 (2009) no. 1, pp. 199-238. doi : 10.5802/aif.2429. http://www.numdam.org/articles/10.5802/aif.2429/
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