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Quantization of a massive orbit of a generalized Poincaré group. (Quantification d’une orbite massive d’un groupe de Poincaré généralisé.) (French) Zbl 0883.22016

Summary: Let \(G\) be the generalized Poincaré group \(\mathbb{R}^{n+1} \times SO_0 (n,1)\) and \({\mathcal O}\) be a coadjoint orbit of \(G\) with little group \(SO(n)\). We give a symplectomorphism from \(\mathbb{R}^{2n} \times {\mathcal O}'\) to \({\mathcal O}\), where \({\mathcal O}'\) is a coadjoint orbit of \(SO(n)\). When \({\mathcal O}\) is entire and associated to a unitary irreducible representation \(\pi\) of \(G\), we construct a Weyl correspondence on \({\mathcal O}\) adapted to \(\pi\).

MSC:

22E46 Semisimple Lie groups and their representations
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
22E70 Applications of Lie groups to the sciences; explicit representations
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