On \(S_n\)-invariant conformal blocks vector bundles of rank one on \(\overline{M}_{0,n}\) (Q2634731)

Let \(\mathbb{V}(\mathfrak{g},\vec{\lambda},l)\) be the vector bundle of conformal blocks, associated to a simple Lie algebra \(\mathfrak{g}\) and \(n\)-tuple \(\vec{\lambda}\) of dominant weights for \(\mathfrak{g}\) at level \(l\), on the moduli space \(\overline{M}_{0,n}\), of stable \(n\)-pointed rational curves. Their first Chern classes, the conformal blocks divisors \(\mathbb{D}(\mathfrak{g},\vec{\lambda},l)\), are base point free, and lie in the cone of nef divisor. The paper under review firstly classifies all vector bundles of conformal blocks for \(sl_n\), with \(S_n\)-invariants weights \(\mathbb{V}(sl_n,\lambda^n,l)\), then the author shows that the cone generated by the corresponding \(\mathbb{D}(sl_n,\lambda^n,l)\) is polyhedral, generated by level one divisors \(\mathbb{D}(sl_n,\omega_i^n,1)\), where \(2\leq i\leq \lfloor\frac{n}{2}\rfloor\).