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

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. 
@article{TMF_2000_123_3_a3,
     author = {I. V. Shirokov},
     title = {Darboux coordinates on $K$-orbits and the spectra of {Casimir} operators on {Lie} groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {407--423},
     publisher = {mathdoc},
     volume = {123},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a3/}
}
TY  - JOUR
AU  - I. V. Shirokov
TI  - Darboux coordinates on $K$-orbits and the spectra of Casimir operators on Lie groups
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 407
EP  - 423
VL  - 123
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a3/
LA  - ru
ID  - TMF_2000_123_3_a3
ER  - 
%0 Journal Article
%A I. V. Shirokov
%T Darboux coordinates on $K$-orbits and the spectra of Casimir operators on Lie groups
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 407-423
%V 123
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a3/
%G ru
%F TMF_2000_123_3_a3
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/