$s{l}_n$ level 1 conformal blocks divisors on ${\bar{M}}_{0,n}$

We study a family of semiample divisors on the moduli space ${\bar{M}}_{0,n}$ that come from the theory of conformal blocks for the Lie algebra $s{l}_n$ and level 1. The divisors we study are invariant under the action of $S_n$ on ${\bar{M}}_{0,n}$. We compute their classes and prove that they generate extremal rays in the cone of symmetric nef divisors on ${\bar{M}}_{0,n}$. In particular, these divisors define birational contractions of ${\bar{M}}_{0,n}$, which we show factor through reduction morphisms to moduli spaces of weighted pointed curves defined by Hassett.