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A Mackey-analogy-based Proof of the Connes-Kasparov Isomorphism for Real Reductive Groups

Afgoustidis, Alexandre (2016), A Mackey-analogy-based Proof of the Connes-Kasparov Isomorphism for Real Reductive Groups. https://basepub.dauphine.fr/handle/123456789/17395

Type
Document de travail / Working paper
External document link
https://arxiv.org/pdf/1602.08891.pdf
Date
2016
Series title
cahier de recherche CEREMADE- Paris-Dauphine
Pages
20
Metadata
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Author(s)
Afgoustidis, Alexandre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG]
Abstract (EN)
We give a new representation-theory based proof of the Connes-Kasparov conjecture for the K-theory of reduced C*-algebras of real reductive Lie groups. Our main tool is a natural correspondence between the tempered representation theory of such a group and that of its Cartan motion group, a semidirect product whose unitary dual and reduced C*-algebra are much more tractable. With that tool in hand, our proof is a natural adaptation of that given by Nigel Higson's work in the complex semi-simple case.
Subjects / Keywords
Higson-Mackey analogy; Tempered representations; Lie group contractions; Reductive Lie groups; Baum-Connes (Connes-Kasparov) isomorphism; Group C*-algebras