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

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.