The Baum-Connes Conjecture and Group Representations

Selected References

Baum, P. F.; Higson, N.; Plymen, R. J. Representation theory of p-adic groups: a view from operator algebras. The mathematical legacy of Harish-Chandra (Baltimore, MD, 1998), 111-149, Proc. Sympos. Pure Math., 68, Amer. Math. Soc., Providence, RI, 2000.   MR
Baum, Paul; Connes, Alain; Higson, Nigel. Classifying space for proper actions and K-theory of group C*-algebras. C*-algebras: 1943-1993 (San Antonio, TX, 1993), 240-291, Contemp. Math., 167, Amer. Math. Soc., Providence, RI, 1994.   MR
Baum, Paul; Higson, Nigel; Plymen, Roger. A proof of the Baum-Connes conjecture for p-adic GL(n). C. R. Acad. Sci. Paris Ser. I Math. 325 (1997), no. 2, 171-176.   MR
Julg, Pierre. La conjecture de Baum-Connes a coefficients pour le groupe Sp(n,1). (French) [The Baum-Connes conjecture with coefficients for the group Sp(n,1)] C. R. Math. Acad. Sci. Paris 334 (2002), no. 7, 533-538.   MR
Julg, Pierre; Kasparov, Gennadi. Operator K-theory for the group SU(n,1). J. Reine Angew. Math. 463 (1995), 99-152.   MR
Kasparov, G. G. Lorentz groups: K-theory of unitary representations and crossed products. (Russian) Dokl. Akad. Nauk SSSR 275 (1984), no. 3, 541-545.   MR
Kasparov, G. G. Operator K-theory and its applications: elliptic operators, group representations, higher signatures, C*-extensions. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 987-1000, PWN, Warsaw, 1984.   MR
Lafforgue, V. Banach KK-theory and the Baum-Connes conjecture. Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 795-812, Higher Ed. Press, Beijing, 2002.   MR
Penington, M. G.; Plymen, R. J. The Dirac operator and the principal series for complex semisimple Lie groups. J. Funct. Anal. 53 (1983), no. 3, 269-286.   MR
Valette, Alain. Dirac induction for semisimple Lie groups having one conjugacy class of Cartan subgroups. Operator algebras and their connections with topology and ergodic theory (Busteni, 1983), 526-555, Lecture Notes in Math., 1132, Springer, Berlin, 1985.   MR
Wassermann, Antony. Une demonstration de la conjecture de Connes-Kasparov pour les groupes de Lie lineaires connexes reductifs. (French) [A proof of the Connes-Kasparov conjecture for connected reductive linear Lie groups] C. R. Acad. Sci. Paris Ser. I Math. 304 (1987), no. 18, 559-562.   MR

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