The Michigan Mathematical Journal

On elliptic Dunkl operators

Pavel Etingof and Xiaoguang Ma

Full-text: Open access

Article information

Michigan Math. J., Volume 57 (2008), 293-304.

First available in Project Euclid: 8 September 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38] 16S32: Rings of differential operators [See also 13N10, 32C38] 20C08: Hecke algebras and their representations
Secondary: 16G99: None of the above, but in this section 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx] 14C20: Divisors, linear systems, invertible sheaves


Etingof, Pavel; Ma, Xiaoguang. On elliptic Dunkl operators. Michigan Math. J. 57 (2008), 293--304. doi:10.1307/mmj/1220879410.

Export citation


  • M. Broué, G. Malle, and R. Rouquier, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998), 127--190.
  • V. Buchstaber, G. Felder, and A. Veselov, Elliptic Dunkl operators, root systems, and functional equations, Duke Math. J. 76 (1994), 885--911.
  • I. Cherednik, Elliptic quantum many-body problem and double affine Knizhnik--Zamolodchikov equation, Comm. Math. Phys. 169 (1995), 441--461.
  • ------, Double affine Hecke algebras, London Math. Soc. Lecture Note Ser., 319, Cambridge Univ. Press, Cambridge, 2005.
  • C. F. Dunkl and E. M. Opdam, Dunkl operators for complex reflection groups, Proc. London Math. Soc. (3) 86 (2003), 70--108.
  • P. Etingof, Cherednik and Hecke algebras of varieties with a finite group action, preprint, math.QA/0406499.
  • P. Etingof, W. L. Gan, and A. Oblomkov, Generalized double affine Hecke algebras of higher rank, J. Reine Angew. Math. 600 (2006), 177--201.
  • P. Etingof, A. Oblomkov, and E. Rains, Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces, Adv. Math. 212 (2007), 749--796.
  • M. Geck and G. Malle, Reflection groups, a contribution to the handbook of algebra, preprint, arXiv:math/0311012.
  • S. Lang, Abelian varieties, Springer-Verlag, New York, 1983.
  • D. Mumford, Abelian varieties, Oxford University Press, Oxford, 1970.
  • S. Sahi, Nonsymmetric Koornwinder polynomials and duality, Ann. of Math. (2) 150 (1999), 267--282.