Conformal blocks divisors and points on curves

I'll discuss a relation between certain divisors on the moduli space of stable rational pointed curves arising in conformal field theory, and geometric invariant theory quotients generically parameterizing configurations of points on Veronese curves. This correspondence shows, in particular, that a symmetry in the representation theory of the special linear group can be viewed as a form of Gale duality first proven by Goppa in the context of algebraic coding theory.