Geodesic
Darboux coordinates on $K$-orbits and the spectra of Casimir operators on Lie groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 407-423 
I. V. Shirokov. Darboux coordinates on $K$-orbits and the spectra of Casimir operators on Lie groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 407-423. http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a3/
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     title = {Darboux coordinates on $K$-orbits and the spectra of {Casimir} operators on {Lie} groups},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We propose an algorithm for obtaining the spectra of Casimir ce Lie groups. We prove that the existence of the normal polarization associated with a linear functional on the Lie algebra is necessary and sufficient for the transition to local canonical Darboux coordinates $(p,q)$ on the coadjoint representation orbit that is linear in the “momenta”. We show that the $\lambda$-representations of Lie algebras are used, in particular, in integrating differential equationsthe quantization of the Poisson bracket on the coalgebra in canonical coordinates.

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