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We consider a conjecture that identifies two types of base point freedivisors on $\bar{M}_{0,n}$. The first arises from Gromov-Witten theory of aGrassmannian. The second comes from first Chern classes of vector bundlesassociated to simple Lie algebras in type A. Here we reduce this conjecture on$\bar{M}_{0,n}$ to the same statement for $n=4$. A reinterpretation leads to aproof of the conjecture on $\bar{M}_{0,n}$ for a large class, and we givesufficient conditions for the non-vanishing of these divisors.

On an equivalence of divisors on $\bar{M}_{0,n}$ from Gromov-Witten theory and conformal blocks