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Book Review

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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?)

  • 1. M. Atiyah and W. Schmid, A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 42 (1977), 1-62. MR 463358
  • 2. V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568-640. MR 21942
  • 3. Armand Borel and Nolan R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, vol. 94, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 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. Mogens Flensted-Jensen, Discrete series for semisimple symmetric spaces, Ann. of Math. (2) 111 (1980), no. 2, 253–311. MR 569073, https://doi.org/10.2307/1971201
  • 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. Rebecca A. Herb, Fourier inversion and the Plancherel theorem for semisimple real Lie groups, Amer. J. Math. 104 (1982), no. 1, 9–58. MR 648480, https://doi.org/10.2307/2374067
  • 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. David A. Vogan Jr., Representations of real reductive Lie groups, Progress in Mathematics, vol. 15, Birkhäuser, Boston, Mass., 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 halb-einfacher Gruppen durch lineare Transformationen. I, Math. Z. 23 (1925), no. 1, 271–309 (German). MR 1544744, https://doi.org/10.1007/BF01506234
  • 15. E. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. of Math. (2) 40 (1939), no. 1, 149–204. MR 1503456, https://doi.org/10.2307/1968551

Review Information:

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