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Kissin, Edward and Shulman, Victor S. (2016) Representations of nilpotent groups on spaces with indefinite metric. Journal of Integral Equations and Operator Theory. ISSN 0378-620X
The paper studies the structure of J-unitary representations of connected nilpotent groups on Πk-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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