Monodromy of A-hypergeometric functions

Abstract

Using Mellin-Barnes integrals we give a method to compute elements of the monodromy group of an A-hypergeometric system of differential equations. The method works under the assumption that the A-hypergeometric system has a basis of solutions consisting of Mellin-Barnes integrals. Hopefully these elements generate the full monodromy group, but this has only been verified in some special cases.