First syzygies of irreducible A-hypergeometric quotients

An A-hypergeometric system is not irreducible, if its parameter vector is resonant. In this paper, we present a way of computing a finite system of generators of the first syzygy module of an irreducible A-hypergeometric quotient. In particular, if the semigroup generated by A is simplicial and scored, then an explicit system of generators is given.