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On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorAfgoustidis, Alexandre
dc.date.accessioned2021-11-30T15:09:16Z
dc.date.available2021-11-30T15:09:16Z
dc.date.issued2020
dc.identifier.issn0012-7094
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22323
dc.language.isoenen
dc.subjectCartan motion groupen
dc.subjectcontractions of Lie groupsen
dc.subjectdeformation of representationsen
dc.subjectMackey analogyen
dc.subjectMackey–Higson bijectionen
dc.subjectreal reductive groupsen
dc.subjecttempered representationsen
dc.subject.ddc519en
dc.titleOn the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenAttached to any reductive Lie group G is a "Cartan motion group" G0 − a Lie group with the same dimension as G, but a simpler group structure. A natural one-to-one correspondence between the irreducible tempered representations of G and the unitary irreducible representations of G0, whose existence had been suggested by Mackey in the 1970s, has recently been described by the author. In the present notes, we use the existence of a family of groups interpolating between G and G0 to realize the bijection as a deformation: for every irreducible tempered representation π of G, we build, in an appropriate Fr\'echet space, a family of subspaces and evolution operators that contract π onto the corresponding representation of G0.en
dc.relation.isversionofjnlnameDuke Mathematical Journal
dc.relation.isversionofjnlvol169en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2020-04
dc.relation.isversionofjnlpages897-960en
dc.relation.isversionofdoi10.1215/00127094-2019-0071en
dc.relation.isversionofjnlpublisherDuke University Pressen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-11-30T15:03:00Z
hal.author.functionaut


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