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 Mat. Sb. (N.S.), 1982, Volume 118(160), Number 2(6), Pages 173–183 (Mi msb2247)

Equivalence of holomorphically induced representations of Lie groups with an Abelian normal subgroup

A. A. Zaitsev

Abstract: 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.
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English version:
Mathematics of the USSR-Sbornik, 1983, 46:2, 171–182

Bibliographic databases:

UDC: 519.46
MSC: Primary 22E45; Secondary 22E60

Citation: A. A. Zaitsev, “Equivalence of holomorphically induced representations of Lie groups with an Abelian normal subgroup”, Mat. Sb. (N.S.), 118(160):2(6) (1982), 173–183; Math. USSR-Sb., 46:2 (1983), 171–182

Citation in format AMSBIB
\Bibitem{Zai82} \by A.~A.~Zaitsev \paper Equivalence of holomorphically induced representations of Lie groups with an Abelian normal subgroup \jour Mat. Sb. (N.S.) \yr 1982 \vol 118(160) \issue 2(6) \pages 173--183 \mathnet{http://mi.mathnet.ru/msb2247} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=658787} \zmath{https://zbmath.org/?q=an:0501.22016|0518.22011} \transl \jour Math. USSR-Sb. \yr 1983 \vol 46 \issue 2 \pages 171--182 \crossref{https://doi.org/10.1070/SM1983v046n02ABEH002763}