Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 2798319
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Ivan Cherednik
Title: Double affine Hecke algebras
Additional book information: London Mathematical Society, Lecture Note Series, 319, xii+434 pp., ISBN 978-0-521-609180, US$79.00$

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

  • Ivan Cherednik, A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1991), no. 2, 411–431. MR 1128220, DOI 10.1007/BF01243918
  • Ivan Cherednik, Double affine Hecke algebras, Knizhnik-Zamolodchikov equations, and Macdonald’s operators, Internat. Math. Res. Notices 9 (1992), 171–180. MR 1185831, DOI 10.1155/S1073792892000199
  • Ivan Cherednik, Induced representations of double affine Hecke algebras and applications, Math. Res. Lett. 1 (1994), no. 3, 319–337. MR 1302647, DOI 10.4310/MRL.1994.v1.n3.a4
  • Ivan Cherednik, Double affine Hecke algebras and Macdonald’s conjectures, Ann. of Math. (2) 141 (1995), no. 1, 191–216. MR 1314036, DOI 10.2307/2118632
  • Ivan Cherednik, Macdonald’s evaluation conjectures and difference Fourier transform, Invent. Math. 122 (1995), no. 1, 119–145. MR 1354956, DOI 10.1007/BF01231441
  • Ivan Cherednik, Nonsymmetric Macdonald polynomials, Internat. Math. Res. Notices 10 (1995), 483–515. MR 1358032, DOI 10.1155/S1073792895000341
  • Ivan Cherednik, Lectures on Knizhnik-Zamolodchikov equations and Hecke algebras, Quantum many-body problems and representation theory, MSJ Mem., vol. 1, Math. Soc. Japan, Tokyo, 1998, pp. 1–96. MR 1724948
  • Ivan Cherednik and Viktor Ostrik, From double Hecke algebra to Fourier transform, Selecta Math. (N.S.) 9 (2003), no. 2, 161–249. MR 1993484, DOI 10.1007/s00029-003-0329-3
  • V. G. Drinfel′d, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR 934283
  • Pavel I. Etingof, Igor B. Frenkel, and Alexander A. Kirillov Jr., Lectures on representation theory and Knizhnik-Zamolodchikov equations, Mathematical Surveys and Monographs, vol. 58, American Mathematical Society, Providence, RI, 1998. MR 1629472, DOI 10.1090/surv/058
  • I. B. Frenkel and N. Yu. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), no. 1, 1–60. MR 1163666
  • G. J. Heckman, An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math. 103 (1991), no. 2, 341–350. MR 1085111, DOI 10.1007/BF01239517
  • N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of ${\mathfrak {p}}$-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5–48. MR 185016
  • Michio Jimbo and Tetsuji Miwa, Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, vol. 85, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1995. MR 1308712
  • V. G. Knizhnik and A. B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984), no. 1, 83–103. MR 853258, DOI 10.1016/0550-3213(84)90374-2
  • V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1993. MR 1245942, DOI 10.1017/CBO9780511628832
  • Gail Letzter, Quantum zonal spherical functions and Macdonald polynomials, Adv. Math. 189 (2004), no. 1, 88–147. MR 2093481, DOI 10.1016/j.aim.2003.11.007
  • George Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), no. 3, 599–635. MR 991016, DOI 10.1090/S0894-0347-1989-0991016-9
  • I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144
  • I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Astérisque 237 (1996), Exp. No. 797, 4, 189–207. Séminaire Bourbaki, Vol. 1994/95. MR 1423624
  • I. G. Macdonald, Orthogonal polynomials associated with root systems, Sém. Lothar. Combin. 45 (2000/01), Art. B45a, 40. MR 1817334
  • I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts in Mathematics, vol. 157, Cambridge University Press, Cambridge, 2003. MR 1976581, DOI 10.1017/CBO9780511542824
  • Masatoshi Noumi, Macdonald’s symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces, Adv. Math. 123 (1996), no. 1, 16–77. MR 1413836, DOI 10.1006/aima.1996.0066
  • S. N. M. Ruijsenaars, Complete integrability of relativistic Calogero-Moser systems and elliptic function identities, Comm. Math. Phys. 110 (1987), no. 2, 191–213. MR 887995
  • F. A. Smirnov, Form factors in completely integrable models of quantum field theory, Advanced Series in Mathematical Physics, vol. 14, World Scientific Publishing Co., Inc., River Edge, NJ, 1992. MR 1253319, DOI 10.1142/1115

  • Review Information:

    Reviewer: Eric M. Opdam
    Affiliation: KdV Institute for Mathematics, University of Amsterdam, The Netherlands
    Reviewer: Jasper V. Stokman
    Affiliation: KdV Institute for Mathematics, University of Amsterdam, The Netherlands
    Journal: Bull. Amer. Math. Soc. 46 (2009), 143-150
    Published electronically: September 15, 2008
    Additional Notes: The work of J. V. Stokman was supported by a VIDI-grant of the Netherlands Organization for Scientific Research (NWO)
    Review copyright: © Copyright 2008 American Mathematical Society