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

@article{Afgoustidis2016OnTA,
title={On the analogy between real reductive groups and Cartan motion groups: A proof of the Connes-Kasparov isomorphism},
author={Alexandre Afgoustidis},
journal={Journal of Functional Analysis},
year={2016},
volume={277},
pages={2237-2258}
}

Abstract 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… Expand