Representations of nilpotent groups on spaces with indefinite metric (Q526745)

This paper is a continuation of the work [J. Funct. Anal. 269, No. 8, 2564--2610 (2015; Zbl 1322.22013)] of the authors in which they studied the cohomology of nilpotent groups, normal cocycles and the extensions of representations generated by cocycles of these groups. The authors of the paper under review study some general properties and the structure of finite-dimensional \(J\)-unitary representations of connected nilpotent groups on Pontryagin spaces. These are the representations on a Hilbert space preserving a quadratic form ``with a finite number of negative squares''. They show that such representations can be constructed as double extensions of finite-dimensional representations by unitary ones. They also investigate the problem of the decomposition of these representations and give some necessary and sufficient conditions for them to be non-\(J\)-decomposable. Finally, they show that all non-\(\Pi\)-decomposable representations of commutative groups are primary.