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Unitary representations for two real forms of a semisimple Lie algebra: A theory of comparison. (English) Zbl 0531.22012

Lie group representations I, Proc. Spec. Year, Univ. Md., College Park 1982-83, Lect. Notes Math. 1024, 1-29 (1983).
[For the entire collection see Zbl 0511.00011.]
Let \(G_ 0\) be a real semi-simple simply connected Lie group admitting a maximal compactly embedded subgroup \(K_ 0\) such that \((G_ 0,K_ 0)\) is an irreducible Hermitian symmetric pair. The main goal of the article is to describe a correspondence between special unitary representations of \(G_ 0\times G_ 0\) and of \(G\), where \(G\) denotes the simply connected complex Lie group such that \(Lie(G)=Lie(G_ 0)\otimes_{{\mathbb{R}}}{\mathbb{C}}\).
Reviewer: J.OesterlĂ©.

MSC:

22E46 Semisimple Lie groups and their representations

Citations:

Zbl 0511.00011