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 | References | Similar Articles | Additional Information
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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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