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Book Review

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Book Information:

Author: V. S. Varadarajan
Title: Harmonic analysis on real reductive groups
Additional book information: Lecture Notes in Math., vol. 576, Springer-Verlag, Berlin, Heidelberg, New York, 1977, 521 pp., $17.20.

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. J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. MR 171173
  • 4. Harish-Chandra, (a) Discrete series for semi-simple Lie groups. I, II, Acta Math. 113 (1965), 241-318; 116 (1966), 1-111.
    Harish-Chandra, (b) Harmonic analysis on reductive p-adic groups, Lecture Notes in Math., vol. 162, Springer-Verlag, Berlin and New York, 1970. MR 414797

    Harish-Chandra, (c) Harmonic analysis on real reductive groups. I. The theory of the constant term, J. Functional Analysis 19 (1975), 104-204. MR 399356

  • 5. Rebecca A. Herb, Characters of averaged discrete series on semisimple real Lie groups, Pacific J. Math. 80 (1979), no. 1, 169–177. MR 534706
  • 6. T. Hirai, Invariant eigendistributions of Laplace operators on real simple Lie groups. IV, Characters of discrete series for Sp(n, R), Japan. J. Math. 3 (1977), 1-48. MR 578896
  • 7. R. Langlands, The dimension of spaces of automorphic forms, Algebraic Groups and Discontinuous Subgroups, Proc. Sympos. Pure Mathematics, vol. 9, Amer. Math. Soc., Providence, R.I., 1966, pp. 253-257. MR 212135
  • 8. G. Mackey, The theory of group representations, Lecture Notes, Univ. of Chicago, 1955. (Republished, Univ. of Chicago Press, 1975.)
  • 9. M. S. Narasimhan and K. Okamoto, An analogue of the Borel-Weil theorem for Hermitian symmetric pairs of noncompact type, Ann. of Math. (2) 91 (1970), 486-511. MR 274657
  • 10. R. Parthasarathy, Dirac operators and the discrete series, Ann. of Math. (2) 96 (1972), 1-30. MR 318398
  • 11. W. Schmid, (a) On a conjecture of Langlands, Ann. of Math. (2) 93 (1971), 1-42. MR 286942
    W. Schmid, (b) On the characters of the discrete series, Invent. Math. 30 (1975), 47-144. MR 396854

  • 12. G. Warner, Harmonic analysis on semi-simple Lie groups. I, II, Springer-Verlag, New York, 1972. MR 498999
  • 12. 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: Rebecca A. Herb
Journal: Bull. Amer. Math. Soc. 1 (1979), 398-401
DOI: https://doi.org/10.1090/S0273-0979-1979-14614-7
American Mathematical Society