On an Equivalence of Divisors on (M)over-bar(0,n) from Gromov-Witten Theory and Conformal Blocks

We consider a conjecture that identifies two types of base point free divisors on (M) over bar (0,n). The first arises from Gromov-Witten theory of a Grassmannian. The second comes from first Chern classes of vector bundles associated with simple Lie algebras in type A. Here we reduce this conjecture on (M) over bar (0,n) to the same statement for n = 4. A reinterpretation leads to a proof of the conjecture on (M) over bar (0,n) for a large class, and we give sufficient conditions for the non-vanishing of these divisors.