Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution

Abstract

The paper is devoted to non-Schlesinger isomonodromic deformations for resonant Fuchsian systems. There are very few explicit examples of such deformations in the literature. In this paper we construct a new example of the non-Schlesinger isomonodromic deformation for a resonant Fuchsian system of order 5 by using middle convolution for a resonant Fuchsian system of order 2. Moreover, it is known that middle convolution is an operation that preserves Schlesinger's deformation equations for non-resonant Fuchsian systems. In this paper we show that Bolibruch's non-Schlesinger deformations of resonant Fuchsian systems are, in general, not preserved by middle convolution.

References in corpus (8)

• Hodge theory of the middle convolution
• Middle Convolution and Heun's Equation
• Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System
• Fourier transform and middle convolution for irregular D-modules
• Fractional calculus of Weyl algebra and Fuchsian differential equations
• Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients
• Twisted Euler transform of differential equations with an irregular singular point
• Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution