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Intertwining operators and unitary representations. I. (English) Zbl 0683.22010

The problem of classifying the irreducible unitary representations of a semisimple Lie group G comes down to finding out whether some intertwining operators are semidefinite. In their preceding five works the authors have introduced some formulas to solve the latter problem and have used them for classifying UIR’s in certain cases: SU(N,2), some other groups of real rank two, Langlands quotients obtained from maximal parabolic subgroups. But in these works there were no proofs of the formulas. In the paper reviewed the authors give the derivations of these formulas - when G has a compact Cartan subgroup.
Reviewer: V.F.Molchanov

MSC:

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