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Corpus ID: 124428678

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

@article{Afgoustidis2016AMB,
title={A Mackey-Analogy based Proof of the Connes-Kasparov Isomorphism for Real Reductive Groups},
author={Alexandre Afgoustidis},
journal={arXiv: Operator Algebras},
year={2016}
}

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… Expand