Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions I

In the present paper we discuss the general facts, concerning the Schlesinger system: the (\tau)-function, the local factorization of solutions of Fuchsian equations and holomorphic deformations. We introduce the terminology “isoprincipal” for the deformations of Fuchsian equations with general (not necessarily non-resonant) matrix coefficients, corresponding to solutions of the Schlesinger system.