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Book Review

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Book Information:

Authors: N. Ja. Vilenkin and A. U. Klimyk
Title: Representation of Lie groups and special functions
Additional book information: Kluwer Acad. Publ., Dordrecht, $804.50 (set). Vol. 1: Simplest Lie groups, special functions and integral transforms, vol. 72, 1991, xxiv + 608 pp., $408.00, ISBN 0-7923-1466-2; Vol. 2: Class I representations, special functions, and integral transforms, vol. 74, 1992, xviii + 607 pp., $397.00, ISBN 0-7923-1492-1; Vol. 3: Classical and quantum groups and special functions, vol. 75, 1992, xx + 634 pp., $397.00, ISBN 0-7923-1493-X,

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

  • 1. R. A. Askey, T. H. Koornwinder and W. Schempp, eds., Special functions: Group theoretical aspects and applications, Reidel, 1984. MR 85i:22003
  • 2. V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. (2) 48 (1947), 568-640. MR 9:133a
  • 3. J. Dieudonné, Special functions and linear representations of Lie groups, Regional Conference Series in Math. 42, American Mathematical Society, 1980. MR 81b:22002
  • 4. J. Faraut, Analyse harmonique et fonctions spéciales, in: Deux cours d'analyse harmonique, Birkhaüser, Boston, 1987, pp. 1-151. CMP 19:15
  • 5. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia Math. Appl., 35, Cambridge Univ. Press, Cambridge, 1990. MR 91d:33034
  • 6. I. M. Gel'fand and Z. Ja. \v{S}apiro, Representations of the group of rotations in three-dimensional space and their applications, Amer. Math. Soc. Transl. (2) 2 (1956), 207-316. MR 17:875d
  • 7. Harish-Chandra, Spherical functions on a semi-simple Lie group I, Amer. J. Math. 80 (1958), 241-310. MR 20:925
  • 8. G. J. Heckman, Hypergeometric and spherical functions, in: Harmonic analysis and special functions on symmetric spaces, Academic Press, 1994. MR 96j:22019
  • 9. A. U. Klimyk, Matrix Elements and Clebsch-Gordan Coefficients of Representations of Groups, ``Naukova Dumka'', Kiev, 1979, (in Russian). MR 80j:22019
  • 10. E. Koelink, 8 Lectures on quantum groups and q-special functions, Revista Colombiana de Matemáticas 30:2 (1996), 93-180. CMP 97:14
  • 11. T. H. Koornwinder, Krawtchouk polynomials, a unification of two different group theoretic interpretations, SIAM J. Math. Anal. 13 (1982), 1011-1023. MR 84f:33022
  • 12. I. G. Macdonald, Spherical Functions on a Group of $p$-adic Type, Publ. Ramanujan Inst. 2, Univ. Madras, India, 1971. MR 55:826
  • 13. I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Séminaire Bourbaki 797 1994-95; Astérisque 237 (1996), 189-207. CMP 97:05
  • 14. W. Miller, Jr., Lie theory and special functions, Academic Press, 1968. MR 41:8736
  • 15. W. Miller, Jr., Symmetry and separation of variables, Encyclopedia of Mathematics and its Applications 4, Addison-Wesley, 1977. MR 57:744
  • 16. M. Noumi and T. Sugitani, Quantum symmetric spaces and related $q$-orthogonal polynomials, in: Group Theoretical Methods in Physics (A. Arima et al., eds.), World Scientific, 1995, pp. 28-40. MR 97h:33033
  • 17. J. D. Talman, Special functions, a group theoretical approach, based on lectures by Eugene P. Wigner, Benjamin, 1968. MR 39:511
  • 18. A. Terras, Harmonic analysis on symmetric spaces and applications I, II, Springer, 1985, 1988. MR 87f:22010;MR 89k:22017
  • 19. N. Ja. Vilenkin, Special Functions and Theory of Group Representations, Izdat. ``Nauka'', Moscow, 1965, Transl. Math. Monographs, Vol. 22, Amer. Math. Soc, Providence, R. I.,1968. MR 35:420; MR 37:5429
  • 20. N. Ya. Vilenkin and A. U. Klimyk, Representations of Lie groups, and special functions (Russian), in: Noncommutative Harmonic Analysis 2 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Moscow, 1990, pp. 145-268, 270; translation in: A. A. Kirillov (ed.), Representation Theory and Noncommutative Harmonic Analysis, Encyclopaedia of Mathematical Sciences 59, Springer, 1995, pp. 137-259. CMP 96:03; MR 92k:22010
  • 21. N. Ja. Vilenkin and A. U. Klimyk, Representation of Lie Groups and Special Functions. Recent Advances, Mathematics and its Applications 316, Kluwer Academic Publishers, 1994. CMP 96:07
  • 22. A. Wawrzynczyk, Group representations and special functions, Reidel, 1984. MR 85e:33010
  • 23. E. P. Wigner, Group theory and its application to the quantum mechanics of atomic spectra, Academic Press, New York, 1959. MR 21:5442

Review Information:

Reviewer: Erik Koelink
Affiliation: University of Amsterdam
Email: koelink@wins.uva.nl
Reviewer: Tom H. Koornwinder
Affiliation: University of Amsterdam
Email: thk@wins.uva.nl
Journal: Bull. Amer. Math. Soc. 35 (1998), 265-270
MSC (1991): Primary 33E80, 22E30
DOI: https://doi.org/10.1090/S0273-0979-98-00757-5
Review copyright: © Copyright 1998 American Mathematical Society
American Mathematical Society