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Banach KK-theory and Baum-Connes conjecture. (English) Zbl 0997.19003

Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press. 795-812 (2002).
Summary: The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group \(C^*\)-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series representations of connected semi-simple Lie groups.
For the entire collection see [Zbl 0993.00022].

MSC:

19K35 Kasparov theory (\(KK\)-theory)
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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