Théorie de Mackey et méthode des orbites selon M. Duflo. (Mackey theory and orbit method according to M. Duflo)
type: Item
instance of: scholarly article
title: Théorie de Mackey et méthode des orbites selon M. Duflo. (Mackey theory and orbit method according to M. Duflo)
zbMATH Open document ID: 0582.22010
published in: Expositiones Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 3931305
zbMATH Keywords: unitary representations
zbMATH Keywords: Kirillov orbit method
zbMATH Keywords: induced representations
zbMATH Keywords: metaplectic group
zbMATH Keywords: algebraic groups
zbMATH Keywords: Plancherel formula
author: Alain Guichardet
MaRDI profile type: Publication
Recommended article: Méthode des orbites pour les représentations de longueur finie. (The orbit method for representations of finite length)
Recommended article: Méthode des orbites pour les représentations de longueur finie. II
Recommended article: Q3243199
Recommended article: Le théorème de Burnside sur le comptage des orbites et quelques applications. (Burnside theorem on the computation f orbits and some applications)
Recommended article: Q3341527
Recommended article: Q3139066
description: scientific article; zbMATH DE number 3931305