About the Rationality of the Knizhnik-Zamolodchikov Equation Solution

Abstract

In the paper the solution of KZ system (n=4, m=2) is constructed in the explicit form in terms of the hypergeometric functions. We proved that the corresponding solution is rational when the parameter $\rho$ is integer. We show that in the case (n=4, m=5, $\rho$ is integer) the corresponding KZ system hasn't got a rational solution.