Geodesic
Remarks on geometric quantization of $R$-matrix type Poisson brackets
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 241-248 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {1997},
     volume = {112},
     number = {2},
     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/

[1] D. Gurevich, D. Panyushev, Duke Math. J, 73:2 (1994), 249–255 | DOI | MR | Zbl

[2] M. Semenov-Tyan-Shansky, Publ. RIMS, Kyoto Univ., 21 (1985), 1237–1260 | DOI | MR

[3] S. Khoroshkin, A. Radul, V. Rubtsov, Commun. Math. Phys., 152 (1993), 299–315 | DOI | MR | Zbl

[4] V. Drinfeld, “Quantum groups”, Proc. ICM, V. 1 (Berkeley), Am. Math. Soc., 1986, 789–920 | MR

[5] J. H. Lu, A. Weinstein, J. Differ. Geom., 31 (1990), 501–526 | DOI | MR | Zbl

[6] S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, New York, 1978 | MR | Zbl

[7] A. A. Kirillov, Elementy teorii predstavlenii, Nauka, M., 1972 | MR

[8] I. Vaisman, J. Math. Phys., 32:12 (1991), 3339–3345 | DOI | MR | Zbl

[9] A. Lichnerovicz, J. Differ. Geom., 12 (1977), 253–300 | DOI | MR

[10] D. Gurevich, V. Rubtsov, N. Zobin, J. Geom. Phys., 9:1 (1992), 25–44 | DOI | MR | Zbl