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Une démonstration de la conjecture of Connes-Kasparov pour les groupes de Lie linéaires connexes réductifs. (A proof of the Connes-Kasparov conjecture for connected reductive linear Lie groups). (French) Zbl 0615.22011
In J. Funct. Anal. 53, 269-286 (1983; Zbl 0542.22013), M. G. Penington and the reviewer verified the Connes-Kasparov conjecture for complex semisimple groups G, by assembling the Fourier components of the twisted Dirac operator on G/K. The author extends this method to linear reductive groups. The technical difficulties increase greatly, and this note is a miniature tour de force.
Reviewer: R.J.Plymen

MSC:
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
46L80 \(K\)-theory and operator algebras (including cyclic theory)
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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