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Irreducible characters and semisimple coadjoint orbits. (English) Zbl 1478.22011

Let \((\mathcal{O}, \Gamma)\) be a semisimple orbital parameter for a non-compact real reductive Lie group \(G_{\mathbb{R}}\). The orbit method aims to attach a unitary representation \(\pi(\mathcal{O}, \Gamma)\) to the parameter \((\mathcal{O}, \Gamma)\). The article under review gives a geometric character formula for \(\pi(\mathcal{O}, \Gamma)\), extending the earlier existing formula obtained by Rossmann and Duflo when \(\pi(\mathcal{O}, \Gamma)\) is tempered. As explained in the paper, the motivation came from abstract harmonic analysis questions and branching problems.

MSC:

22E46 Semisimple Lie groups and their representations
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