ON THE QUANTIZATION OF ISOMONODROMIC DEFORMATIONS ON THE TORUS

The quantization of isomonodromic deformation of a meromorphic connect ion on the torus is shown to lead directly to the Knizhnik-Zamolodchik ov-Bernard equations in the same way as the problem on the sphere lead s to the system of Knizhnik-Zamolodchikov equations. The Poisson brack et required for a Hamiltonian formulation of isomonodromic deformation s is naturally induced by the Poisson structure of Chern-Simons theory in a holomorphic gauge fixing. This turns out to be the origin of the appearance of twisted quantities on the torus.