THE 2×2 MATRIX SCHLESINGER SYSTEM AND THE BELAVIN–POLYAKOV–ZAMOLODCHIKOV SYSTEM

摘要

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 matrices. This generalizes Suleimanov’s result on the Painlev′e equations. We consider the properties of the solutions, which are expressible in terms of the Riemann theta function.