Integral Solutions to Schlesinger Equations

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 mul...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 208; no. 2; pp. 229 - 239
Main Author Leksin, V. P.
Format Journal Article
LanguageEnglish
Published New York Springer US 02.07.2015
Springer
Subjects
Mathematics
Mathematics and Statistics
Fundamental Matrix
Monodromy Matrix
Holomorphic Vector Bundle
Riemann Sphere
Vector Bundle
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-015-2440-3