Geodesic
Remarks on geometric quantization of $R$-matrix type Poisson brackets
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 241-248

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We check the Vaisman condition of geometric quantization for $R$-matrix type Poisson pencil on a coadjoint orbit of a compact semisimple Lie group. It is shown that this condition is not satisfied for hermitian symmetric spaces. We also construct some examples when the Vaisman condition takes place. 
@article{TMF_1997_112_2_a2,
     author = {A. Yu. Kotov},
     title = {Remarks on geometric quantization of $R$-matrix type {Poisson} brackets},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {241--248},
     publisher = {mathdoc},
     volume = {112},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a2/}
}
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A. Yu. Kotov. Remarks on geometric quantization of $R$-matrix type Poisson brackets. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 241-248. http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a2/