The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras

Abstract

The purpose of this paper is to make a further contribution to the Mackey bijection for a complex reductive group G G , between the tempered dual of G G and the unitary dual of the associated Cartan motion group. We shall construct an embedding of the C ∗ C^* -algebra of the motion group into the reduced C ∗ C^* -algebra of G G , and use it to characterize the continuous field of reduced group C ∗ C^* -algebras that is associated to the Mackey bijection. We shall also obtain a new characterization of the Mackey bijection using the same embedding.