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The unitary dual of \(G_ 2\). (English) Zbl 0808.22003

Let \(G\) be the simply connected simple Lie group with the Lie algebra which is the split real form of the complex simple Lie algebra of type \(G_ 2\). In this paper the author determines the unitary dual of \(G\). This is a nice illustration of the general methods to check unitarity of irreducible Harish-Chandra modules developed by the author.

MSC:

22E46 Semisimple Lie groups and their representations
17B20 Simple, semisimple, reductive (super)algebras
22E60 Lie algebras of Lie groups
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