Geodesic
The~$2{\times}2$ matrix Schlesinger system and the~Belavin--Polyakov--Zamolodchikov system
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 2, pp. 191-203

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We show that the Belavin–Polyakov–Zamolodchikov equation of the minimal model of conformal field theory with the central charge $c=1$ for the Virasoro algebra is contained in a system of linear equations that generates the Schlesinger system with $2{\times}2$ matrices. This generalizes Suleimanov's result on the Painlevé equations. We consider the properties of the solutions, which are expressible in terms of the Riemann theta function.
Keywords: Belavin–Polyakov–Zamolodchikov equation, Schlesinger system, Painlevé equation
Mots-clés : Garnier system. 
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     author = {D. P. Novikov},
     title = {The~$2{\times}2$ matrix {Schlesinger} system and {the~Belavin--Polyakov--Zamolodchikov} system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {191--203},
     publisher = {mathdoc},
     volume = {161},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a4/}
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D. P. Novikov. The~$2{\times}2$ matrix Schlesinger system and the~Belavin--Polyakov--Zamolodchikov system. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 2, pp. 191-203. http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a4/