IRREDUCIBILITY AND REDUCIBILITY OF LAURICELLA'S SYSTEM OF DIFFERENTIAL EQUATIONS ED AND THE JORDAN-POCHHAMMER DIFFERENTIAL EQUATION EJP

摘要

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