Theoretical and Mathematical Physics

, Volume 106, Issue 1, pp 50–60 | Cite as

On the Veselov-Felder reconstruction formula in the theory of Calogero-Sutherland operators

  • V. A. Golubeva
  • V. P. Leksin


Matsuo [1] and Cherednik [2] proposed an elegant construction connecting the solutions of generalized Knizhnik-Zamolodchikov (KZ) equations with the eigenfunctions of Calogero-Sutherland operators associated with the same root system. Considering rational KZ equations, Veselov [3] and Felder [4] simplified the arguments used in [1, 2] and derived the reconstruction formula for the root system An−1. This gives the solution of the KZ equation in terms of eigenfunctions of the Calogero operator. In this paper, for any reduced and irreducible root system, we directly verify the Matsuo-Cherednik statement for the connection of solutions to KZ equations to the eigenfunctions of Calogero-Sutherland operators. We extend the Felder-Veselov reconstruction formula to these root systems.


Root System Reconstruction Formula Irreducible Root System 
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  1. 1.
    A. Matsuo,Invent. Math.,110, 95–121 (1992).Google Scholar
  2. 2.
    I. Cherednik,Adv. Math.,106, 65–95 (1994).Google Scholar
  3. 3.
    G. Felder and A. Veselov,Commun. Math. Phys.,160, 259–274 (1994).Google Scholar
  4. 4.
    A. P. Veselov,Teor. Mat. Fiz.,98, 524–535 (1994).Google Scholar
  5. 5.
    Ch. F. Dunkl,Trans. Amer. Math. Soc.,311, 167–183 (1989).Google Scholar
  6. 6.
    E. Date, M. Jimbo, A. Matsuo, and T. Miwa, “Hypergeometric-type integrals and ℁ (2, ℂ) Knizhnik-Zamolodchikov equation,” Preprint, RIMS (1989).Google Scholar
  7. 7.
    A. Matsuo,Commun. Math. Phys.,134, 65–77 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. A. Golubeva
    • 1
  • V. P. Leksin
    • 1
  1. 1.VINITI The Colomna Teacher-Training CollegeUSSR

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