INTEGRAL SOLUTIONS TO SCHLESINGER EQUATIONS

摘要

It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order p on the Riemann spheres with upper triangular monodromy are reduced to multidimensional linear homogeneous (p = 2) and inhomogeneous (≥3) Pfaffian systems. For components of the solutions to the multidimensional linear Pfaffian systems (p = 2) we obtain integral representations of hypergeometric type and expressions in quadratures close to the hypergeometric Schlesinger equations describing deformations of upper triangular Fuchsian systems of order p = 3. Bibliography: 11 titles.