THE MACKEY BIJECTION FOR COMPLEX REDUCTIVE GROUPS AND CONTINUOUS FIELDS OF REDUCED GROUP C*-ALGEBRAS

Nigel Higson, Angel RomÁn

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)580-602
Number of pages23
JournalRepresentation Theory
Volume24
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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