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


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.


Difference Equation Quantum Group Quantum Dynamical Joint Work Weighted Trace 


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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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