The 2×2 matrix Schlesinger system and the Belavin-Polyakov-Zamolodchikov system

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 2×2 tmatrices. This generalizes Suleimanov’s result on the Painleve equations. We consider the properties of the solutions, which are expressible in terms of the Riemann theta function.