Determinant structure for tau-function of holonomic deformation of linear differential equations

Abstract

In our previous works [16,17], a relationship between Hermite's two approximation problems and Schlesinger transformations of linear differential equations has been clarified. In this paper, we study τ-functions associated with holonomic deformations of linear differential equations by using Hermite's two approximation problems. As a result, we present a determinant formula for the ratio of τ-functions (τ-quotient).