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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : Painlevé equation, Garnier system. 
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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/

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