We investigate the behavior of vector bundles of conformal blocks for $sp_{ 2\ell}$ at level one on $\bar{ M}_{ 0,n}$. We show their first Chern classes are equivalent to conformal blocks divisors for $sl_2$ at level $\ell$ if and only if the corresponding vector bundles have rank one or zero, and all become equal when the Lie algebra $\ell$ is large enough. As a consequence of these results, we conclude the cone generated by these divisors is polyhedral.
Categories: math.AG