Shift operators of the Dotsenko-Fateev equation and its higher order versions

TL;DR

This paper constructs shift operators for the Dotsenko-Fateev equation and related higher-order Fuchsian equations, enabling analysis of their reducibility and structural properties.

Contribution

It introduces explicit shift operators for these differential equations, connecting them through addition and middle convolution, and advances understanding of their reducible cases.

Findings

Constructed shift operators for orders 3 to 6 equations

Connected equations via addition and middle convolution

Analyzed reducibility conditions

Abstract

We find shift operators for the Dotsenko-Fateev equation, which is a differential equation of order 3, and for the three Fuchsian differential equations of order 4, 5 and 6, respectively, which are connected with the Dotsenko-Fateev equation via addition and middle convolution. These shift operators are used to study reducible cases.