# Lauricella's $F_C$ with finite irreducible monodromy group

## TL;DR

This paper investigates the specific parameter conditions that lead to finite irreducible monodromy groups for Lauricella's hypergeometric function $F_C$, and explores the structure of these groups.

## Contribution

It provides explicit parameter criteria for finiteness and irreducibility of the monodromy group of Lauricella's $F_C$, and analyzes their structural properties.

## Key findings

- Identifies parameter conditions for finite irreducible monodromy groups
- Characterizes the structure of these monodromy groups
- Enhances understanding of hypergeometric function monodromy representations

## Abstract

We study the conditions under which the monodromy group for Lauricella's hypergeometric function $F_C (a,b,c;x)$ is finite irreducible. We give the conditions in terms of the parameters $a,b,c$. In addition, we discuss the structure of the finite irreducible monodromy group.