Geodesic
Positive polarizations and Abelian ideals in Lie algebras
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 227-240 
A. A. Zaitsev. Positive polarizations and Abelian ideals in Lie algebras. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 227-240. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a7/
@article{SM_1981_40_2_a7,
     author = {A. A. Zaitsev},
     title = {Positive polarizations and {Abelian} ideals in {Lie} algebras},
     journal = {Sbornik. Mathematics},
     pages = {227--240},
     year = {1981},
     volume = {40},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_40_2_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper a theorem on the relative distribution of an Abelian ideal and a positive polarization in a Lie algebra (of general type) is proved. It permits one to extend signficantly the domain of application of a theorem on holomorphically induced representations of Lie groups with an Abelian normal subgroup and a criterion for nontriviality of the representation space given by a polarization, both results obtained earlier by the author. Bibliography: 4 titles.

[1] A. A. Kirillov, Elementy teorii predstavlenii, izd-vo “Nauka”, Moskva, 1977 | MR | Zbl

[2] L. Auslander, B. Kostant, “Quantization and unitary representations of solvable Lie qroups”, Bull. Amer. Math. Soc., 73 (1967), 692–695 | DOI | MR | Zbl

[3] A. A. Zaitsev, “Golomorfno indutsirovannye predstavleniya grupp Li s abelevym normalnym delitelem”, Trudy Mosk. matem. ob-va, 40, 1979, 47–82 | MR

[4] A. A. Zaitsev, “O nezavisimosti predstavleniya ot vybora polyarizatsii dlya grupp s abelevym normalnym delitelem”, Funkts. analiz, 8:4 (1974), 83–84 | MR