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

Higson, Nigel; Román, Angel

doi:10.1090/ert/554

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

Authors: Nigel Higson and Angel Román
Journal: Represent. Theory 24 (2020), 580-602
MSC (2020): Primary 22E45, 46L99
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 , between the tempered dual of and the unitary dual of the associated Cartan motion group. We shall construct an embedding of the -algebra of the motion group into the reduced -algebra of , and use it to characterize the continuous field of reduced group -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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