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Representations of Nilpotent Groups on Spaces with Indefinite Metric

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Abstract

The paper studies the structure of J-unitary representations of connected nilpotent groups on \(\Pi _{k}\)-spaces, that is, the representations on a Hilbert space preserving a quadratic form “with a finite number of negative squares”. Apart from some comparatively simple cases, such representations can be realized as double extensions of finite-dimensional representations by unitary ones. So their study is based on some special cohomological technique. We concentrate mostly on the problems of the decomposition of these representations and the classification of “non-decomposable” ones.

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Authors and Affiliations

  1. STORM, London Metropolitan University, 166-220 Holloway Road, London, N7 8DB, Great Britain

    Edward Kissin

  2. Department of Mathematics, Vologda State University, Vologda, 160000, Russia

    Victor S. Shulman

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  1. Edward Kissin
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  2. Victor S. Shulman
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Correspondence to Edward Kissin.

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Kissin, E., Shulman, V.S. Representations of Nilpotent Groups on Spaces with Indefinite Metric. Integr. Equ. Oper. Theory 87, 81–116 (2017). https://doi.org/10.1007/s00020-016-2337-7

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  • DOI: https://doi.org/10.1007/s00020-016-2337-7

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