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In early eighties, Belavin and Drinfeld showed that nonskewsymmetricclassical r-matrices for simple Lie algebras are classified by combinatorialobjects which are now called Belavin-Drinfeld triples. Later the second authorof the present paper generalized this result to the case of dynamicalr-matrices, and showed that they correspond to generalized Belavin-Drinfeldtriples. The dynamical r-matrix corresponding a triple is given by a certainexplicit formula, which works for any symmetrizable Kac-Moody algebra. Inspecial cases, this formula gives the Felder and the Belavin r-matrix.  In 1994, Felder associated with every dynamical r-matrix a system ofdifferential equations called the KZB equations. In the case of the Felder andBelavin r-matrix, solutions of these equations are known to have arepresentation theoretical presentation, as conformal blocks (i.e. traces ofproducts of intertwining operators between representations of Lie algebras).  In this paper, we propose such a presentation for ANY dynamical r-matrixgiven by the second author's formula. In particular, the paper sheds light onthe Belavin-Drinfeld classical r-matrices of 1984.  This paper begins a series of papers. In the next paper, joint withT.Schedler, we will give an explicit quantization of the dynamical r-matricesfor simple Lie algebras (in particular, Belavin-Drinfeld r-matrices), which hasbeen an open problem for a number of years. In another paper, we plan togeneralize the results of the present paper to quantum groups. This shouldyield quantum KZB equations which involve quantum R-matrices obtained byquantizing the classical r-matrices that appear in this paper.

Twisted traces of intertwiners for Kac-Moody algebras and classical dynamical r-matrices corresponding to generalized Belavin-Drinfeld triples