  We let S denote the ring of polynomial functions on the space of m x n
matrices, and consider the action of the group GL = GL_m x GL_n via row and
column operations on the matrix entries. For a GL-invariant ideal I in S we
show that the linear strands of its minimal free resolution translate via the
BGG correspondence to modules over the general linear Lie superalgebra gl(m|n).
When I is the ideal generated by the GL-orbit of a highest weight vector, we
give a conjectural description of the classes of these gl(m|n)-modules in the
Grothendieck group, and prove that our prediction is correct for the first
strand of the minimal free resolution.
