Irreducibility of the monodromy representation of Lauricella's F_C

2017/03/28 by Goto, Yoshiaki, Matsumoto, Keiji
#32S40 #33C65 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.09401

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.

Related

• Monodromy representations of hypergeometric systems with respect to fundamental series solutions
• The monodromy representation of Lauricella's hypergeometric function F_C
• Lauricella's F_C with finite irreducible monodromy group
• The monodromy representations of local systems associated with Lauricella's F_D
• Groebner basis and singular locus of Lauricella's hypergeometric differential equations