MONODROMY AND PFAFFIAN OF LAURICELLA'S F_D IN TERMS OF THE INTERSECTION FORMS OF TWISTED (CO)HOMOLOGY GROUPS

Abstract

We give the monodromy representation and the Pfaffian system of Lauricella's differential equations annihilating the hypergeometric series F_D(a,b,c; x) of multivariables. Our representation spaces are twisted homology and cohomology groups associated with integrals representing solutions. Without assigning bases to these groups, we express circuit transformations and components of the connection form in terms of the intersection form of the twisted (co)homology groups. Each of them is characterized by an eigenvector of it.