Geodesic
Equivalence of holomorphically induced representations of Lie groups with an Abelian normal subgroup
Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 171-182 
A. A. Zaitsev. Equivalence of holomorphically induced representations of Lie groups with an Abelian normal subgroup. Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 171-182. http://geodesic.mathdoc.fr/item/SM_1983_46_2_a2/
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     title = {Equivalence of holomorphically induced representations of {Lie} groups with an {Abelian} normal subgroup},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a unitary representation of a Lie group given by a positive polarization. Suppose the group contains an Abelian normal subgroup of a suitable sort. It is then shown that if we replace the polarization by a certain new one that contains the corresponding Abelian ideal, the equivalence class of the representation is left unchanged. Bibliography: 5 titles.

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

[2] Kirillov A. A., “Kharaktery unitarnykh predstavlenii grupp Li”, Funkts. analiz, 2:2 (1968), 40–55 | MR | Zbl

[3] Kostant B., “On certain unitary representations which arise from a quantization theory”, Lecture Notes Phys., no. 6, 1970, 237–253 | MR | Zbl

[4] Zaitsev A. A., “Usloviya netrivialnosti gilbertova prostranstva golomorfno indutsirovannogo predstavleniya razreshimoi gruppy Li”, Matem. sb., 112 (154) (1980), 568–587 | MR

[5] Zaitsev A. A., “Polozhitelnye polyarizatsii i abelevy idealy v algebrakh Li”, Matem. sb., 112 (154) (1980), 242–255 | MR