The monodromy representation of Lauricella's hypergeometric function F_C

TL;DR

This paper investigates the monodromy representation of Lauricella's hypergeometric function F_C, using twisted homology groups, fundamental group generators, and intersection forms to understand its analytic continuation properties.

Contribution

It provides explicit generators and relations for the fundamental group and expresses circuit transformations via intersection forms, advancing the understanding of F_C's monodromy.

Findings

Identified generators of the fundamental group of the singular locus complement

Derived relations among these generators

Expressed circuit transformations using intersection forms

Abstract

We study the monodromy representation of the system $E_C$ of differential equations annihilating Lauricella's hypergeometric function $F_C$ of $m$ variables. Our representation space is the twisted homology group associated with an integral representation of $F_C$. We find generators of the fundamental group of the complement of the singular locus of $E_C$, and give some relations for these generators. We express the circuit transformations along these generators, by using the intersection forms defined on the twisted homology group and its dual.