Irreducibility of the monodromy representation of Lauricella's $F_C$

Abstract

Let $E_C$ be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series $F_C$ of $m$ variables. We show that the monodromy representation of $E_C$ is irreducible under our assumption consisting of $2^{m+1}$ conditions for parameters. We also show that the monodromy representation is reducible if one of them is not satisfied.

15 pages

References in corpus (2)

• Twisted cycles and twisted period relations for Lauricella's hypergeometric function F_C
• Monodromy representations of hypergeometric systems with respect to fundamental series solutions