CONTINUITY OF THE MACKEY-HIGSON BIJECTION

Alexandre Afgoustidis; Anne Marie Aubert

doi:10.2140/pjm.2021.310.257

CONTINUITY OF THE MACKEY-HIGSON BIJECTION

Alexandre Afgoustidis
, Anne Marie Aubert

Université Paris Dauphine
Nancy Université
Sorbonne Université

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 (Formula presented) and that of the unitary dual (Formula presented), and then verify that the Mackey–Higson bijection (Formula presented) is continuous.

Original language	English
Pages (from-to)	257-273
Number of pages	17
Journal	Pacific Journal of Mathematics
Volume	310
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2021.310.257
Publication status	Published - 1 Jan 2021
Externally published	Yes

Keywords

Cartan motion group
Fell topology
Mackey–Higson bijection
real reductive groups
tempered representations

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10.2140/pjm.2021.310.257

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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 (Formula presented) and that of the unitary dual (Formula presented), and then verify that the Mackey{\textendash}Higson bijection (Formula presented) is continuous.",

keywords = "Cartan motion group, Fell topology, Mackey{\textendash}Higson bijection, real reductive groups, tempered representations",

author = "Alexandre Afgoustidis and Aubert, \{Anne Marie\}",

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N2 - 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 (Formula presented) and that of the unitary dual (Formula presented), and then verify that the Mackey–Higson bijection (Formula presented) is continuous.

AB - 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 (Formula presented) and that of the unitary dual (Formula presented), and then verify that the Mackey–Higson bijection (Formula presented) is continuous.

KW - Cartan motion group

KW - Fell topology

KW - Mackey–Higson bijection

KW - real reductive groups

KW - tempered representations

UR - https://www.scopus.com/pages/publications/85103089998

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DO - 10.2140/pjm.2021.310.257

M3 - Article

AN - SCOPUS:85103089998

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SP - 257

EP - 273

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

CONTINUITY OF THE MACKEY-HIGSON BIJECTION

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Keywords

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