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 ρ is integer. We show that in the case (n=4, m=5, ρ is integer) the corresponding KZ system hasn't got a rational solution.Mathematics Subject Classification (2000). Primary 35C05; Secondary 20B05, 15A18.

On the factorization formula for fundamental solutions in the inverse spectral transform

“…Note that constructions similar to (1.6) appear also in the theory of Knizhnik-Zamolodchikov equation (see Theorem 3.1 in [46] and see also [45]). Theorem 1.1 is proved in Section 2.…”