Discrete Structure of Some Schlesinger Systems on the Riemann Sphere |
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Authors: | Sergei Oblezin |
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Institution: | (1) Moscow Institute of Physics and Technology, 141700, Institutsky per. 9, Dolgoprudny, Russia;(2) Institute of Theoretical and Experimental Physics, 117259, Bol. Cheremushkinskaya 25, Moscow, Russia |
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Abstract: | In the present work we investigate the group structure of the Schlesinger transformations for isomonodromic deformations of the Fuchsian differential equations. We perform these transformations as isomorphisms between the moduli spaces of the logarithmic sl(N)-connections with fixed eigenvalues of the residues at singular points. We give a geometrical interpretation of the Schlesinger transformations and perform our calculations using the techniques of the modifications of bundles with connections, or, the Hecke correspondences for the loop group SL(N) C(z). |
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Keywords: | Fuchsian differential equations logarithmic connections isomonodromic deformations Schlesinger systems Schlesinger transformations |
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