Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy-preserving symmetry tran sformations of the classical Schlesinger system. Generalizing well-known re sults from the Riemann sphere we construct these transformations for isomon odromic deformations on genus one Riemann surfaces. Their action on the sys tem's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function. (C) 2000 American Insti tute of Physics. [S0022-2488(00)04505-9].