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

2019/08/29 by Higson, Nigel, Roman, Angel · 2 citations
#FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1908.11008

Abstract

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.

Cited by

• A Mackey embedding for reduced C*-algebras of real reductive groups
• Higher Orbital Integrals on Motion Groups and Mackey Deformation

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