The monodromy representation of Lauricella's hypergeometric function F_C

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.

27+2 pages, 3+1 figures

References in corpus (1)

• Twisted cycles and twisted period relations for Lauricella's hypergeometric function F_C

Cited by in corpus (4)

• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• Monodromy representations of hypergeometric systems with respect to fundamental series solutions
• Pfaffian of Appell's hypergeometric system $F_4$ in terms of the intersection form of twisted cohomology groups
• Picard-Vessiot groups of Lauricella's hypergeometric systems $E_C$ and Calabi-Yau varieties arising integral representations