Continuity of the Mackey–Higson bijection

When $G$ is a real reductive group and $G_{0}$ 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 $G_{0}$ . We collect some known facts about the topology of the tempered dual $\tilde{G}$ and that of the unitary dual $\hat{G_{0}}$ , and then verify that the Mackey–Higson bijection $\tilde{G} \to \hat{G_{0}}$ is continuous.

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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

Vol. 310, No. 2, 2021

Alexandre Afgoustidis and Anne-Marie Aubert

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors