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.
Bibliography: 5 titles.

UDC: 519.46

MSC: Primary 22E45; Secondary 22E60

Received: 31.03.1981

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

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