On S n -invariant conformal blocks vector bundles of rank one on {\overline{M}_{0,n}}

For any simple Lie algebra, a positive integer, and n-tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all vector bundles of conformal blocks for \({\mathfrak{sl}_n}\), with S _n -invariant weights, which have rank one. We show that the cone generated by their base point free first Chern classes is polyhedral, generated by level one divisors.