On elliptic Dunkl operators

Preprint, Other literature type English OPEN
Etingof, Pavel ; Ma, Xiaoguang (2007)
  • Publisher: University of Michigan, Department of Mathematics
  • Journal: (issn: 0026-2285)
  • Related identifiers: doi: 10.1307/mmj/1220879410
  • Subject: 13N10 | 16S32 | 14C20 | 14H52 | 20C08 | Mathematics - Representation Theory | 16G99 | Mathematics - Quantum Algebra
    arxiv: Mathematics::Representation Theory | Mathematics::Quantum Algebra

We attach elliptic Dunkl operators to an abelian variety with a finite group action. This generalizes elliptic Dunkl operators for Weyl groups, defined by Buchstaber, Felder, and Veselov in 1994. We show that these operators commute, and use them to define representatio... View more
  • References (13)
    13 references, page 1 of 2

    [BMR] M. Brou´e, G. Malle and R. Rouquier, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998), 127-190.

    [BFV] Buchstaber, V., Felder, G., Veselov, A., Elliptic Dunkl operators, root systems, and functional equations Duke Math.J. 76 (1994) 885-911.

    [Ch1] Cherednik, I., Elliptic quantum many-body problem and double affine KnizhnikZamolodchikov equation. Comm. Math. Phys. 169 (1995), no. 2, 441-461.

    [Ch2] Cherednik, I. Double affine Hecke algebras, London Mathematical Society Lecture Note Series, 319, Cambridge University Press, Cambridge, 2005.

    [Mu] D. Mumford, Abelian varieties, Oxford University Press, 1974.

    [DO] C. F. Dunkl, E. M. Opdam, Dunkl operators for complex reflection groups, Proc. London Math. Soc. (3) 86 (2003), no. 1, 70-108.

    [E] P. Etingof, Cherednik and Hecke algebras of varieties with a finite group action, math.QA/0406499.

    [EGO] Etingof, P., Gan, W. L., Oblomkov, A., Generalized double affine Hecke algebras of higher rank. J. Reine Angew. Math. 600 (2006), 177-201.

    [EOR] P. Etingof, A. Oblomkov, E. Rains, Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces, arXiv:math/0406480, to appear in Advances in Math.

    [GM] M. Geck, G. Malle, Reflection Groups, A Contribution to the Handbook of Algebra, arXiv:math/0311012.

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