This article is cited in 4 papers

Discrete Symmetries of Systems of Isomonodromic Deformations of Second-Order Fuchsian Differential Equations

S. V. Oblezin<sup>ab

a</sup> Moscow Institute of Physics and Technology
^b Independent University of Moscow

Abstract: We compute the discrete affine group of Schlesinger transformations for isomonodromic deformations of a Fuchsian system of second-order differential equations. These transformations are treated as isomorphisms between the moduli spaces of logarithmic $sl(2)$-connections with given eigenvalues of the residues on $\mathbb{P}^1$. The discrete structure is computed with the use of the modification technique for bundles with connections. The result generalizes the well-known classical computations of symmetries of the hypergeometric equation, the Heun equation, and the sixth Painlevé equation.

Keywords: Schlesinger transformations, the Frobenius–Hecke sheaves, Fuchsian systems, the hypergeometric equation, the Heun equation.

UDC: 512.72+515.179

Received: 28.11.2002

DOI: 10.4213/faa106

 English version: Functional Analysis and Its Applications, 2004, 38:2, 111–124

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