Rationality of the Knizhnik-Zamolodchikov equation solution

摘要

We construct an explicit solution of the Knizhnik-Zamolodchikov system with n = 4 and m = 2 in the terms of hypergeometric functions. We prove that this solution is rational when the parameter ρ is integer. We show that the Knizhnik-Zamolodchikov system has no rational solution in the case where n = 5, m = 5, and ρ is integer.