IRREDUCIBILITY AND REDUCIBILITY OF LAURICELLA' S SYSTEM OF DIFFERENTIAL EQUATIONS E_D AND THE JORDAN-POCHHAMMER DIFFERENTIAL EQUATION E_JP

Abstract

Monodromy representations on the solution space of Lauricella' s system of differential equations E_D and the Jordan-Pochhammer differential equation E_JP are studied by using integrals of a multivalued function. We first establish the fact that any solution of E_D and any solution of E_JP are both expressed by the integrals of a multivalued function. Second, a necessary and sufficient condition for the irreducibility is given.