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Bulletin of the American Mathematical Society

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Book Review

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Full text of review: PDF
Book Information:

Author: Anthony W. Knapp
Title: Representation theory of semisimple groups. An overview based on examples
Additional book information: Princeton Mathematics Series, vol. 36, Princeton University Press, Princeton, N. J., 1986, xvii + 773 pp., $75.00. ISBN 0-691-08401-7.

References [Enhancements On Off] (What's this?)

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  • 2. V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568-640. MR 21942
  • 3. A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Princeton Univ. Press, Princeton, N. J., 1980. MR 554917
  • 4. F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97-205. MR 84713
  • 5. M. Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), 253-311. MR 569073
  • 6. I. M. Gelfand and M. A. Naimark, Unitary representations of the Lorentz group, Izv. Akad. Nauk SSSR 11 (1947), 411-504. MR 24440
  • 7. I. M. Gelfand and M. A. Naimark, Unitary representations of the classical groups, Trudy Mat. Inst. Steklov 36, Moscow-Leningrad, 1950. German translation: Akademie-Verlag, Berlin, 1957. MR 46370
  • 8. Harish-Chandra, Discrete series for semi-simple Lie groups. I, Construction of invariant eigendistributions, Acta Math. 113 (1965), 241-318. MR 219665
  • 9. Harish-Chandra, Discrete series for semi-simple Lie groups. II, Explicit determination of the characters, Acta Math. 116 (1966), 1-111. MR 219666
  • 10. R. Herb, Fourier inversion and the Plancherel theorem for semisimple real Lie groups, Amer. J. Math. 104 (1982), 9-58. MR 648480
  • 11. V. S. Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Math., vol 576, Springer-Verlag, Berlin and New York, 1977. MR 473111
  • 12. D. Vogan, Representations of real reductive Lie groups, Birkhäuser, Boston-Basel-Stuttgart, 1981. MR 632407
  • 13. G. Warner, Harmonic analysis on semisimple Lie groups, vols. I and II, Springer-Verlag, Berlin, and New York, 1972.
  • 14. H. Weyl, Theorie der Darstellung kontinuierlicher Gruppen. I, II, III, Math. Z. 23 (1925), 271-309; 24 (1925), 328-376, 377-395. MR 1544744
  • 15. E. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. of Math. (2) 40 (1939), 149-204. MR 1503456

Review Information:

Reviewer: David A. Vogan, Jr.
Journal: Bull. Amer. Math. Soc. 17 (1987), 392-396
DOI: http://dx.doi.org/10.1090/S0273-0979-1987-15612-6