Abstract
It is shown that all irreducible representations of a σ-compact Lie group G have to be finite dimensional provided that for every π in the reduced dual of G the tensor product π ⊗\(\bar \pi \) has a discrete support.
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Kaniuth, E. Characterizing moore groups by tensor products of irreducible representations. Manuscripta Math 42, 1–10 (1983). https://doi.org/10.1007/BF01171742
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DOI: https://doi.org/10.1007/BF01171742