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

MSC:

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

References:

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