Connection coefficients and monodromy representations for a class of Okubo systems of ordinary differential equations

TL;DR

This paper computes connection coefficients and monodromy representations for specific Okubo systems, using Katz operations to explicitly construct solutions and analyze their monodromy, advancing understanding of these differential equations.

Contribution

It introduces a method using Katz operations to explicitly construct Okubo systems and their monodromy representations, solving the connection problem for canonical solutions.

Findings

Explicit connection coefficients for types I, I*, II, III Okubo systems

Construction of monodromy representations for these systems

Application to the connection problem for canonical solutions

Abstract

In this paper, we determine the connection coefficients for Okubo's canonical solution matrix of types ${\rm I}$, ${\rm I}^*$, ${\rm II}$ and ${\rm III}$ in Yokoyama's list.To solve these problems, we investigate a special type of Katz operations for Okubo systems. These operations are used for explicit constructing Okubo systems and their monodromy representations We construct Okubo system and monodromy representations. We further apply their results to the connection problem for canonical solution matrices.