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

Higson, Nigel; Román, Angel

doi:10.1090/ert/554

The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras
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by Nigel Higson and Angel Román

Represent. Theory 24 (2020), 580-602

DOI: https://doi.org/10.1090/ert/554

Published electronically: November 9, 2020

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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.

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