A differential equation with monodromy group $2.J_2$

TL;DR

This paper constructs a sixth order differential equation with a specific complex monodromy group, derived through tensor products and convolutions from a simpler first order equation, revealing deep connections between differential equations and group theory.

Contribution

It introduces a novel sixth order differential equation with monodromy group 2.J_2, obtained via iterative tensor and convolution operations from a basic first order equation.

Findings

The differential equation has monodromy group 2.J_2.

It is constructed through iterative tensor and convolution operations.

The approach links differential equations with complex group structures.

Abstract

We construct a sixth order differential equation having the central extension of $C_2$ by the Hall-Janko group $J_2$ as monodromy group. Moreover it arises from an iterated application of tensor products and convolution operations from a first order differential equation.