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MathSciNet review: 2798319
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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$79.00$

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

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Review Information:

Reviewer: Eric M. Opdam
Affiliation: KdV Institute for Mathematics, University of Amsterdam, The Netherlands
Email: e.m.opdam@uva.nl
Reviewer: Jasper V. Stokman
Affiliation: KdV Institute for Mathematics, University of Amsterdam, The Netherlands
Email: j.v.stokman@uva.nl

Journal: Bull. Amer. Math. Soc. 46 (2009), 143-150
DOI: https://doi.org/10.1090/S0273-0979-08-01208-1
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