Quelques aspects topologiques en analyse harmonique (Q1059811)

The article deals with irreducible representations of Lie groups and with the description of corresponding \(C^*\)-group algebras. It contains a survey of results by the author, of some related results and extensive bibliography. Principal themes are: a generalization of the Mackey- Blattner construction of holomorphically induced representations; quantization of homogeneous dynamical systems with an appropriate generalization of the orbit method by Kirillov-Kostant; applications to irreducible representations of groups of diffeomorphisms; index theory in \(C^*\)-algebras; a description of \(C^*\)-group algebras of some solvable Lie groups.