P. Etingof et O. Schiffmann, Twisted traces of quantum intertwiners and quantum dynamical R-matrices corresponding to generalized Belavin-Drinfeld triples, COMM MATH P, 218(3), 2001, pp. 633-663
We consider weighted traces of products of intertwining operators for quan
tum groups U-q(g), suitably twisted by a "generalized Belavin-Drinfeld trip
le". We derive two commuting sets of difference equations- the (twisted) Ma
cdonald-Ruijsenaars system and the (twisted) quantum Knizhnik-Zamolodchikov
-Bernard (qKZB) system. These systems involve the nonstandard quantum R-mat
rices defined in a previous joint work with T. Schedler ([ESS]). When the g
eneralized Belavin-Drinfeld triple comes from an automorphism of the Lie al
gebra g, we also derive two additional sets of difference equations, the du
al Macdonald-Ruijsenaars system and the dual qKZB equations.