• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

How tempered representations of a semisimple Lie group contract to its Cartan motion group

Afgoustidis, Alexandre (2015), How tempered representations of a semisimple Lie group contract to its Cartan motion group. https://basepub.dauphine.psl.eu/handle/123456789/24540

View/Open
1510.02650v1.pdf (1.205Mb)
Type
Document de travail / Working paper
Date
2015
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
51
Metadata
Show full item record
Author(s)
Afgoustidis, Alexandre cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Abstract (EN)
George W. Mackey suggested in 1975 that there should be analogies between the irreducible unitary representations of a noncompact semisimple Lie group G and those of its Cartan motion group − the semidirect product G 0 of a maximal compact subgroup of G and a vector space. In these notes, I focus on the carrier spaces for these representations and try to give a precise meaning to some of Mackey's remarks. I first describe a bijection, based on Mackey's suggestions, between the tempered dual of G − the set of equivalence classes of irreducible unitary representations which are weakly contained in L 2 (G) − and the unitary dual of G 0. I then examine the relationship between the individual representations paired by this bijection : there is a natural continuous family of groups interpolating between G and G 0 , and starting from the Hilbert space H for an irreducible representation of G, I prove that there is an essentially unique way of following a vector through the contraction from G to G 0 within a fixed Fréchet space that contains H. It then turns out that there is a limit to this contraction process on vectors, and that the subspace of our Fréchet space thus obtained naturally carries an irreducible representation of G 0 whose equivalence class is that predicted by Mackey's analogy.
Subjects / Keywords
Representations of semisimple Lie groups; Lie group contractions; Mackey analogy; Tempered dual

Related items

Showing items related by title and author.

  • Thumbnail
    How tempered representations of a semisimple Lie group contract to its Cartan motion group 
    Afgoustidis, Alexandre (2015) Document de travail / Working paper
  • Thumbnail
    On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations 
    Afgoustidis, Alexandre (2020) Article accepté pour publication ou publié
  • Thumbnail
    On the analogy between real reductive groups and Cartan motion groups. III: A proof of the Connes-Kasparov isomorphism 
    Afgoustidis, Alexandre (2019) Article accepté pour publication ou publié
  • Thumbnail
    On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection 
    Afgoustidis, Alexandre (2021) Document de travail / Working paper
  • Thumbnail
    A Mackey-analogy-based Proof of the Connes-Kasparov Isomorphism for Real Reductive Groups 
    Afgoustidis, Alexandre (2016) Document de travail / Working paper
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo