Geodesic
Quantization and the orbit method
Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", Tome 22 (1984), pp. 37-58 
V. A. Ginzburg. Quantization and the orbit method. Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", Tome 22 (1984), pp. 37-58. http://geodesic.mathdoc.fr/item/INTM_1984_22_a1/
@article{INTM_1984_22_a1,
     author = {V. A. Ginzburg},
     title = {Quantization and the orbit method},
     journal = {Itogi nauki i tehniki. Seri\^a, Matemati\v{c}eskij analiz},
     pages = {37--58},
     year = {1984},
     volume = {22},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTM_1984_22_a1/}
}
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VL  - 22
UR  - http://geodesic.mathdoc.fr/item/INTM_1984_22_a1/
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%T Quantization and the orbit method
%J Itogi nauki i tehniki. Seriâ, Matematičeskij analiz
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A survey is given of the method of orbits which makes it possible to construct irreducible unitary representations of an arbitrary Lie group proceeding from mechanical considerations. After a brief introduction to symplectic geometry, a construction of a representation associated with an orbit of a group in the dual space of its Lie algebra is given. Various generalizations of this construction are discussed.