Elliptic KZ system, braid group of the torus and Vassiliev invariants

We study finite type invariants for links in the product of the torus and the unit interval by means of the monodromy of the elliptic KZ equation. We show that the weight system for the chord diagrams on the torus defined for any representation of the Lie algebra sl(N, C) and a certain projectively flat connection on the torus can be integrated to a link invariant by using the elliptic KZ system.