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Communications in Mathematical Physics

, Volume 218, Issue 3, pp 633–663 | Cite as

Twisted Traces of Quantum Intertwiners¶and Quantum Dynamical R-Matrices¶Corresponding to Generalized Belavin–Drinfeld Triples

  • P. Etingof
  • O. Schiffmann

Abstract:

We consider weighted traces of products of intertwining operators for quantum groups U q (?), suitably twisted by a “generalized Belavin–Drinfeld triple”. We derive two commuting sets of difference equations – the (twisted) Macdonald–Ruijsenaars system and the (twisted) quantum Knizhnik–Zamolodchikov–Bernard (qKZB) system. These systems involve the nonstandard quantum R-matrices defined in a previous joint work with T. Schedler ([ESS]). When the generalized Belavin–Drinfeld triple comes from an automorphism of the Lie algebra ?, we also derive two additional sets of difference equations, the dual Macdonald–Ruijsenaars system and the \textit{dual} qKZB equations.

Keywords

Difference Equation Quantum Group Quantum Dynamical Joint Work Weighted Trace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • P. Etingof
    • 1
  • O. Schiffmann
    • 2
  1. 1.Columbia University, Mathematics Department, 2990 Broadway, New York, NY 10027, USAUS
  2. 2.Yale University, Mathematics Department, 10 Hillhouse Ave., New Haven, CT 06510, USA.¶E-mail: schiffmann@math.yale.eduUS

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