Vol. 310, No. 2, 2021

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Continuity of the Mackey–Higson bijection

Alexandre Afgoustidis and Anne-Marie Aubert

Vol. 310 (2021), No. 2, 257–273
DOI: 10.2140/pjm.2021.310.257
Abstract

When G is a real reductive group and G0 is its Cartan motion group, the Mackey–Higson bijection is a natural one-to-one correspondence between all irreducible tempered representations of G and all irreducible unitary representations of G0. We collect some known facts about the topology of the tempered dual G˜ and that of the unitary dual G0 ̂, and then verify that the Mackey–Higson bijection G˜ G0 ̂ is continuous.

Keywords
real reductive groups, Cartan motion group, tempered representations, Fell topology, Mackey–Higson bijection
Mathematical Subject Classification 2010
Primary: 22E47
Secondary: 22E50
Milestones
Received: 8 November 2019
Revised: 16 November 2020
Accepted: 9 December 2020
Published: 8 March 2021
Authors
Alexandre Afgoustidis
Ceremade
Université Paris-Dauphine
Paris
France
CNRS & Institut Élie Cartan de Lorraine
Université de Lorraine
Vandoeuvre-lès-Nancy
France
Anne-Marie Aubert
Institut de Mathématiques de Jussieu - Paris Rive Gauche
CNRS, Sorbonne Université and Université de Paris
Paris
France