Differential equations associated to the SU (2) WZNW model on elliptic curves

We study the SU (2) WZNW model over a family of elliptic curves. Starting from the formulation developed in [13], we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard equations [1][9]. Our system completely determines the N-point functions and is regarded as a natural elliptic analogue of the system obtained in [12] for the projective line. We also calculate the system for the 1-point functions explicitly. This gives a generalization of the results in [7] for sl(2, ℂ)-characters.