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The duality correspondence of infinitesimal characters. (English) Zbl 0854.22017

The correspondence of the infinitesimal characters of representations which occur in Howe’s duality theorem is determined and the lowest \(K\)-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact are identified.
Reviewer: V.L.Popov (Moskva)

MSC:

22E46 Semisimple Lie groups and their representations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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