Geodesic
Discrete Symmetries of Systems of Isomonodromic Deformations of Second-Order Fuchsian Differential Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 38-54

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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. 
@article{FAA_2004_38_2_a3,
     author = {S. V. Oblezin},
     title = {Discrete {Symmetries} of {Systems} of {Isomonodromic} {Deformations} of {Second-Order} {Fuchsian} {Differential} {Equations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {38--54},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a3/}
}
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S. V. Oblezin. Discrete Symmetries of Systems of Isomonodromic Deformations of Second-Order Fuchsian Differential Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 38-54. http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a3/