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Article Dans Une Revue Journal of Functional Analysis Année : 2019

On the analogy between real reductive groups and Cartan motion groups. III: A proof of the Connes-Kasparov isomorphism

Résumé

Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov “conjecture” for the K-theory of reduced group $C^\ast$-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.
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Dates et versions

hal-01284057 , version 1 (20-12-2021)

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Paternité - Pas d'utilisation commerciale

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Citer

Alexandre Afgoustidis. On the analogy between real reductive groups and Cartan motion groups. III: A proof of the Connes-Kasparov isomorphism. Journal of Functional Analysis, 2019, 277 (7), pp.2237-2258. ⟨10.1016/j.jfa.2019.02.023⟩. ⟨hal-01284057⟩
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