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Book Review
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Book Information
Author(s):
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:
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- 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.
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- 12.
- I. G. Macdonald, Spherical Functions on a Group of
-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
-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
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- 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
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Additional Information:
Reviewer(s):
Erik
Koelink
Affiliation:
University of Amsterdam
Email:
koelink@wins.uva.nl
Reviewer(s):
Tom
H.
Koornwinder
Affiliation:
University of Amsterdam
Email:
thk@wins.uva.nl
Review Information:
Journal:
Bull. Amer. Math. Soc.
35
(1998),
265-270.
MSC
(1991):
Primary 33E80, 22E30
DOI:
10.1090/S0273-0979-98-00757-5
PII:
S 0273-0979(98)00757-5
Copyright of article:
Copyright
1998,
American Mathematical Society
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