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Book Information
Author(s):
Ivan Cherednik
Title:
Double affine Hecke algebras
Additional book information:
London Mathematical Society,
Lecture Note Series, 319, xii+434 pp.,
US$79.00,
ISBN 978-0-521-609180
References:
-
- [1]
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- [3]
- I. Cherednik, Induced representations of double affine Hecke algebras and applications, Math. Res. Lett. 1 (1994), 319-337. MR 1302647 (96i:17022)
- [4]
- I. Cherednik, Double affine Hecke algebras and Macdonald's conjectures, Ann. of Math. (2) 141 (1995), no. 1, 191-216. MR 1314036 (96m:33010)
- [5]
- I. Cherednik, Macdonald's evaluation conjectures and difference Fourier transform, Invent. Math. 122 (1995), no. 1, 119-145. MR 1354956 (98i:33027a)
- [6]
- I. Cherednik, Nonsymmetric Macdonald polynomials, Internat. Math. Res. Notices 1995, no. 10, 483-515. MR 1358032 (97f:33032)
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- I. Cherednik, Lectures on Knizhnik-Zamolodchikov equations and Hecke algebras. In: Quantum many-body problems and representation theory, 1-96, MSJ Mem., 1, Math. Soc. Japan, Tokyo, 1998. MR 1724948 (2001g:20004)
- [8]
- I. Cherednik, V. Ostrik, From double affine Hecke algebra to Fourier transform, Selecta Math. (N.S.) 9 (2003), no. 2, 161-249. MR 1993484 (2004f:20011)
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- V.G. Drinfel'd, Quantum Groups. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 798-820, Amer. Math. Soc., Providence, RI, 1987. MR 934283 (89f:17017)
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- P.I. Etingof, I.B. Frenkel, A.A. Kirillov Jr., Lectures on representation theory and Knizhnik-Zamolodchikov equations. Mathematical Surveys and Monographs, 58. Amer. Math. Soc., Providence, RI, 1998. MR 1629472 (2001b:32028)
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- I.B. Frenkel, N. Yu. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), no. 1, 1-60. MR 1163666 (94c:17024)
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- G.J. Heckman, An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math. 103 (1991), 341-350. MR 1085111 (92i:33012)
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- N. Iwahori, H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of
 -adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5-48. MR 0185016 (32:2486) - [14]
- M. Jimbo, T. Miwa, Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, 85. Amer. Math. Soc., Providence, RI, 1995. MR 1308712 (96e:82037)
- [15]
- V.G. Knizhnik, A.B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984), 83-103. MR 853258 (87h:81129)
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- V.E. Korepin, N.M. Bogoliubov, A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press 1993. MR 1245942 (95b:81224)
- [17]
- G. Letzter, Quantum zonal spherical functions and Macdonald polynomials, Adv. Math. 189, no. 1 (2004), 88-147. MR 2093481 (2005i:33019)
- [18]
- G. Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), no. 3, 599-635. MR 991016 (90e:16049)
- [19]
- I.G. Macdonald, Symmetric functions and Hall polynomials, second edition. Oxford Math. Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1005. MR 1354144 (96h:05207)
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- I.G. Macdonald, Affine Hecke algebras and orthogonal polynomials. Séminaire Bourbaki, Vol. 1994/95. Astérisque No. 237 (1996), Exp. No. 797, 4, 189-207. MR 1423624 (99f:33024)
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- I.G. Macdonald, Orthogonal polynomials associated with root systems, Sém. Lothar. Combin. 45 (2000/01), Art. B45a, 40 pp. MR 1817334 (2002a:33021)
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Additional Information:
Reviewer(s):
Eric
M.
Opdam
Affiliation:
KdV Institute for Mathematics, University of Amsterdam, The Netherlands
Email:
e.m.opdam@uva.nl
Reviewer(s):
Jasper
V.
Stokman
Affiliation:
KdV Institute for Mathematics, University of Amsterdam, The Netherlands
Email:
j.v.stokman@uva.nl
Review Information:
Journal:
Bull. Amer. Math. Soc.
46
(2009),
143-150.
MSC
(2000):
Primary 32G34, 33D80;
Secondary 33D52, 20C08
DOI:
10.1090/S0273-0979-08-01208-1
PII:
S 0273-0979(08)01208-1
Posted:
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)
Copyright of article:
Copyright
2008,
American Mathematical Society
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