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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 $ 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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Additional Information

Nigel Higson
Affiliation: Department of Mathematics, Penn State University, University Park, Pennsylvania 16802

Angel Román
Affiliation: Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
Address at time of publication: Department of Mathematics, William and Mary, Williamsburg, Virginia 23185
Email: arroman@wm.edu

DOI: https://doi.org/10.1090/ert/554
Received by editor(s): November 3, 2019
Received by editor(s) in revised form: June 19, 2020
Published electronically: November 9, 2020
Article copyright: © Copyright 2020 American Mathematical Society