On the minimal free resolution of the universal ring for resolutions of length two

Hochster established the existence of a commutative noetherian ring and a universal resolution U of the form such that for any commutative noetherian ring S and any resolution V equal to 0→Se→Sf→Sg→0, there exists a unique ring homomorphism with . In the present paper we assume that f=e+g and we find the minimal resolution of by free B-modules, where B is a polynomial ring over the field of rational numbers. The modules of the resolution are described in terms of Schur functors. The graded strands of the differential are described in terms of Pieri maps.