Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.Arthur, Harmonic analysis on the Schwartz space of a reductive Lie group II, mimeographed notes, Yale University, 1975.
M.F. Atiyah & W. Schmid, A geometric construction of the discrete series for semi-simple Lie groups, Inventiones Math. 42 (1977), 1–62.
S. Baaj & P. Julg, Théorie bivariante de Kasparov et opérateurs non bornés dans les C*-modules hilbertiens, C.R.Acad.Sc. Paris 296, Sér.I (1983), 875–878.
P.Baum & A.Connes, Geometric K-theory for Lie groups and foliations, to appear in Proc. 1983 U.S.-Japan seminar, "Geometric methods in Operator Algebras".
N. Bourbaki, Groupes et algèbres de Lie (Chap.IV,V,VI), Hermann (Paris), 1968.
J. Dixmier, C*-algebras, North-Holland (Amsterdam), 1982.
S.Helgason, Differential geomerty and symmetric spaces, Monographs in Pure & Applied Math.12, Academic Press, 1962.
G.G. Kasparov, The index of invariant elliptic operators, K-theory and Lie group representations, Dok.Akad.Nauk.USSR. 268 (1983), 533–537.
G.G.Kasparov, Lorentz groups: K-theory of unitary representations and crossed products, Preprint Chernogolovka, 1983.
G.G.Kasparov, Operator K-theory and its applications: elliptic operators, group representations, higher signatures, C*-extensions, to appear in Proc. International Congress of Math. Warsaw, 1983.
A.W. Knapp & E.M. Stein, Intertwining operators for semi-simple Lie groups, Ann. of Math. 93 (1971), 489–578.
R.L. Lipsman, The dual topology for the principal and discrete series on semi-simple Lie groups, Trans.A.M.S. 152 (1970), 399–417.
R.L. Lipsman, On the characters and equivalence of continuous series representations, J.Math.Soc.Japan 23(1971), 452–480.
R.L.Lipsman, Group representations, Springer Lect. Notes in Maths. 388, 1974.
D. Milicic’, Topological representation of the group C*-algebra of SL2(IR), Glasnik Matem. 6(26)(1971), 231–246.
R. Parthasarathy, Dirac operator and the discrete series, Ann. of Math. 96 (1972), 1–30.
M.G. Penington & R.J. Plymen, The Dirac operator and the principal series for complex semi-simple Lie groups, Journ. of Funct. Anal. 53 (1983), 269–286.
A.Valette, K-theory for the reduced C*-algebra of a semisimple Lie group with real rank 1 and finite centre, to appear in Quart. Journ. Math. (Oxford).
N.R. Wallach, Cyclic vectors and irreducibility for principal series representations, Trans.Amer.Math.Soc.158(1971), 107–113.
N.R. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker (New-York), 1973.
G.Warner, Harmonic analysis on semi-simple Lie groups I, II, Springer 1972.
A.Wassermann, A proof of the Connes-Kasparov conjecture for linear reductive Lie groups, preprint (University of Liverpool), Dec. 1983.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verleg
About this paper
Cite this paper
Valette, A. (1985). Dirac induction for semi-simple lie groups having one conjugacy class of cartan subgroups. In: Araki, H., Moore, C.C., Stratila, ŞV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074908
Download citation
DOI: https://doi.org/10.1007/BFb0074908
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15643-7
Online ISBN: 978-3-540-39514-0
eBook Packages: Springer Book Archive