Generic representations are induced from square-integrable representations

Lipsman, Ronald L.

doi:10.1090/S0002-9947-1984-0752506-9

Generic representations are induced from square-integrable representations
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Trans. Amer. Math. Soc. 285 (1984), 845-854 Request permission

Abstract:

It is proven for arbitrary real algebraic groups that the generic irreducible unitary representation is induced from a square-integrable representation (modulo the projective kernel). This generalizes the well-known result for reductive groups that the generic representations are either discrete series, or induced from discrete series (modulo the nilradical) representations of cuspidal parabolic subgroups.

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