THE EXISTENCE OF EQUIVARIANT PURE FREE RESOLUTIONS

Let A = K[x(1),...,x(m)] be a polynomial ring in m variables and let d = (d(0) < ... < d(m)) be a strictly increasing sequence of m + 1 integers. Boij and Soderberg conjectured the existence of graded A-modules M of finite length having pure free resolution of type d in the sense that for i = 0,...,m the i-th syzygy module of M has generators only in degree d(i). This paper provides a construction, in characteristic zero, of modules with this property that are also GL(m)-equivariant. Moreover, the construction works over rings of the form A circle times(K) B where A is a polynomial ring as above and B is an exterior algebra.