A paper by M.L. Whippman in Rep. Math. Phys. 5 (1974), 81, mentions at the bottom of the second page ''the possible occurrence of non-unitary representations that arise when reducing a direct product of representations of a non-compact group''. I'd like to see a simple example of this situation. The context is unitary representations, but it seems to me that the direct product of unitary representations cannot lead to this.
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$\begingroup$ What is a direct product of unitary representations? $\endgroup$– Mikael de la SalleCommented Jun 1, 2016 at 13:43
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$\begingroup$ @MikaeldelaSalle: The canonical representation on the tensor product of the two representation spaces. $\endgroup$– Arnold NeumaierCommented Jun 1, 2016 at 15:39
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