Divisors on $\overline{M}_{0,n}$ from conformal blocks

Given a simple Lie algebra $\mathfrak{g}$, a positive
integer $\ell$ called the level, and an appropriately chosen
$n$-tuple of dominant integral weights $\overline{\lambda}$ of level
$\ell$, one can define a vector bundle on the stacks
$\overline{M}_{g,n}$ whose fibers are the so-called vector spaces of
conformal blocks. On $\overline{M}_{0,n}$, first Chern classes of
these vector bundles turn out to be semi-ample divisors, and so define
morphisms. In this talk I will discuss the simplest examples of
these divisors, and show that they can be treated entirely
combinatorially. I'll show that every morphism we know of on
$\overline{M}_{0,n}$ comes from one of these divisors and even some
that we didn't.