Geodesic
Symmetries of the 4-matrices Schlesinger system
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 92-108

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All types of symmetries, such as a permutation of parameters, Schlesinger and Okamoto transformations are considered. The new form of Schlesinger system and the action of modular group on the corresponding linear system are studied, the geometrical meaning of the Okamoto transformation is discussed. 
@article{ZNSL_2000_269_a6,
     author = {M. V. Babich},
     title = {Symmetries of the 4-matrices {Schlesinger} system},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {92--108},
     publisher = {mathdoc},
     volume = {269},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a6/}
}
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M. V. Babich. Symmetries of the 4-matrices Schlesinger system. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 16, Tome 269 (2000), pp. 92-108. http://geodesic.mathdoc.fr/item/ZNSL_2000_269_a6/