On the analogy between real reductive groups and Cartan motion groups. III: A proof of the Connes-Kasparov isomorphism
Afgoustidis, Alexandre (2019), On the analogy between real reductive groups and Cartan motion groups. III: A proof of the Connes-Kasparov isomorphism, Journal of Functional Analysis, 277, 7, p. 2237-2258. 10.1016/j.jfa.2019.02.023
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01284057
Journal nameJournal of Functional Analysis
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov “conjecture” for the K-theory of reduced group C∗-algebras seemed, in the case of reductive Lie groups, to be a cohomological echo of a conjecture of George Mackey concerning the rigidity of representation theory along the deformation from a real reductive group to its Cartan motion group. For complex semisimple groups, Nigel Higson established in 2008 that Mackey's analogy is a real phenomenon, and does lead to a simple proof of the Connes-Kasparov isomorphism. We here turn to more general reductive groups and use our recent work on Mackey's proposal, together with Higson's work, to obtain a new proof of the Connes-Kasparov isomorphism.
Subjects / KeywordsGroup C*-algebras; Baum-Connes (Connes-Kasparov) isomorphism; Reductive Lie groups; Lie group contractions; Tempered representations; Higson-Mackey analogy
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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