THE MACKEY BIJECTION FOR COMPLEX REDUCTIVE GROUPS AND CONTINUOUS FIELDS OF REDUCED GROUP C*-ALGEBRAS

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