A property of polarization

  • A. A. Zaitsev


Let G be a real Lie group with the Lie algebra g, and let f be a real linear functional on g. It is established that if Ker f does not contain nonzero ideals of the algebra g, then the existence of a total positive complex polarization for f implies that the Lie algebra of the stationary subgroup of the functional f in g is reductive.


Nonzero Ideal Complex Polarization Stationary Subgroup Real Linear Positive Complex 
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Literature cited

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    A. A. Zaitsev, “On the independence of representation from the choice of polarization for groups with an Abelian normal subgroup,” Funkts. Analiz,8, No. 4, 83–84 (1974).Google Scholar
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    A. A. Kirillov, “Unitary representations of nilpotent Lie groups,” Usp. Mat. Nauk,17, No. 4, 57–101 (1962).Google Scholar
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    L. Auslander and B. Kostant, “Quantization and representations of solvable Lie groups,” Bull. Am. Math. Soc.,73, No. 5, 692–695 (1967).Google Scholar
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    A. M. Perelomov, “Coherent states for the Lobachevskian plane,” Funkts. Analiz,7, No.3, 57–66 (1973).Google Scholar
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    J. P. Serre, Lie Algebras and Lie Groups, W. A. Bejamin, New York (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • A. A. Zaitsev
    • 1
  1. 1.Central Scientific-Research Institute for Industrial BuildingsUSSR

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