UNIFORMIZATION SYSTEMS OF EQUATIONS WITH SINGULARITIES ALONG THE DISCRIMINANT SETS OF COMPLEX REFLECTION GROUPS OF RANK THREE

摘要

K. Saito [RIMS K?ky?roku Bessatsu 287 (1977), 117-137] introduced uniformization systems of equations with singularities along free divisors. The purpose of this paper is to construct such systems for the case of finite irreducible complex reflection groups of rank three. Each of them is essentially a system of linear differential equations of Fuchsian type in two variables with three linearly independent solutions. As a special case, uniformization systems of equations whose monodoromy groups are the finite irreducible complex reflection groups themselves are obtained in a closed form. This case has already been treated by Haraoka and the first author in [Funkcial. Ekvac. 53 (2010), 435-488] and our study is a generalization of their result.