Keywords
- Weyl Group
- Unitary Representation
- Parabolic Subgroup
- Discrete Series
- Principal Series
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. DUFLO, Représentations irréductibles des groupes semi-simples complexes, in Analyse Harmonique sur les Groupes de Lie, Lecture Notes in Mathematics 497 (1975), 26–88, Springer-Verlag, New-York.
M. DUFLO, Représentations unitaires irréductibles des groupes simples complexes de rang deux, to appear.
HARISH-CHANDRA, Discrete series for semisimple groups II, Acta Math. 116 (1966), 1–111.
H. HECHT and W. SCHMID, A proof of Blattner's conjecture, Inventiones Math. 31 (1975), 129–154.
T. HIRAI, On irreducible representations of the Lorentz group of n-th order, Proc. Japan Acad. 38 (1962), 83–87.
A.W. KNAPP, Weyl group of a cuspidal parabolic, Ann. Sci. Ecole Norm. Sup. 8 (1975), 275–294.
A.W. KNAPP and E.M. STEIN, The existence of complementary series, in Problems in Analysis, a Symposium in Honor of Salomon Bochner, R.C. Gunning (ed.), 249–259, Princeton University Press, Princeton, New Jersey, 1970.
A.W. KNAPP and E.M. STEIN, Intertwining operators for semisimple groups, Ann. of Math. 93 (1971), 489–578.
A.W. KNAPP and E.M. STEIN, Singular integrals and the principal series III, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 4622–4624.
A.W. KNAPP and E.M. STEIN, Singular integrals and the principal series IV, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 2459–2461.
A.W. KNAPP and G. ZUCKERMAN, Classification of irreducible tempered representations of semisimple Lie groups, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 2178–2180.
B. KOSTANT, On the existence and irreducibility of certain series of representations, in Lie groups and their representations, Summer School of the Bolyai Janos Mathematical Society, I.M. Gelfand (ed.) 231–329, Wiley, New-York, 1975.
H. KRALJEVIČ, Representations of the universal covering group of the group SU(n, 1), Glasnik Mat. 8 (1973), 23–72.
R.P. LANGLANDS, On the classification of irreducible representations of real algebraic groups, mimeographed notes, Institute for Advanced Study, Princeton, New Jersey, 1973.
E.M. STEIN, Analysis in matrix spaces and some new representations of SL (N, C), Ann. of Math. 86 (1967), 461–490.
P. TROMBI, The tempered spectrum of a real semisimple Lie group, Amer. J. Math., to appear.
M. TSUCHIKAWA, On the representations of SL (3, C), III, Proc. Japan Acad. 44 (1968), 130–132.
I.J. VAHUTINSKII, Unitary representations of GL (3, R), Math. Sbornik 75 (117) (1968), 303–320 (in Russian).
N. WALLACH, Cyclic vectors and irreducibility for principal series representations, Trans. Amer. Math. Soc. 158 (1971), 107–113.
D.P. ZELOBENKO, Harmonic analysis on semisimple complex Lie groups, Ed. Nauka, Moscow, 1975 (in Russian).
D.P. ZELOBENKO and M.A. NAIMARK, A characterization of completely irreducible representations of a semisimple complex Lie group, Soviet Math. Dokl. 7 (1966), 1403–1406.
G. ZUCKERMAN, Tensor products of finite and infinite dimensional representations of semisimple Lie groups, to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1977 Springer-Verlag
About this paper
Cite this paper
Knapp, A.W., Zuckerman, G. (1977). Classification theorems for representations of semisimple lie groups. In: Carmona, J., Vergne, M. (eds) Non-Commutative Harmonic Analysis. Lecture Notes in Mathematics, vol 587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087919
Download citation
DOI: https://doi.org/10.1007/BFb0087919
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08245-3
Online ISBN: 978-3-540-37365-0
eBook Packages: Springer Book Archive
