Théorie de Mackey et méthode des orbites selon M. Duflo. (Mackey theory and orbit method according to M. Duflo)
The paper provides a careful and readable introduction to the work of M. Duflo and his school on the construction of unitary representations of general Lie groups. As background, the author recalls the essentials of the Kirillov orbit method, of Mackey's theory of induced representations, and basic facts about the metaplectic group in the form needed. He goes on to an exposition of two versions of Duflo's theory. The first one is a ''Mackey theory for algebraic groups'', not a true ''orbit method'' in the sense of Kirillov, although coadjoint orbits do enter into the parametrization of the irreducible unitary representations. The second one is a true ''orbit method'', which provides a very satisfactory relation between coadjoint orbits, irreducible unitary representations, and their infinitesimal and global character. The representations so constructed suffice for the Plancherel formula, but Duflo's work on the Plancherel formula is not included in the exposition under review.
scientific article; zbMATH DE number 3931305