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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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 PDF
Represent. Theory 24 (2020), 580-602 Request permission


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
  • MR Author ID: 238781
  • ORCID: 0000-0001-9661-1663
  • 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
  • ORCID: 0000-0001-6467-9516
  • Email:
  • Received by editor(s): November 3, 2019
  • Received by editor(s) in revised form: June 19, 2020
  • Published electronically: November 9, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 580-602
  • MSC (2020): Primary 22E45, 46L99
  • DOI:
  • MathSciNet review: 4171564