Unitary representations induced from maximal parabolic subgroups. (English) Zbl 0614.22004

From the introduction: ”It is known that the problem of classifying the irreducible unitary representations of a linear connected semisimple Lie group G comes down to deciding which Langlands quotients J(MAN,\(\sigma\),\(\nu)\) are infinitesimally unitary. Here MAN is any cuspidal parabolic subgroup, \(\sigma\) any discrete series or nondegenerate limit of discrete series representation of M and \(\nu\) any complex-valued linear functional on the Lie algebra of A satisfying certain positivity and symmetry properties. The authors determine which Langlands quotients are infinitesimally unitary under the condition that G is simple, that dim A\(=1\) and that G is neither split \(F_ 4\) nor split \(G_ 2.\)”
Reviewer: B.Speh


22E46 Semisimple Lie groups and their representations
22D10 Unitary representations of locally compact groups
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