Conformal Blocks in type C at level one

We investigate the behavior of vector bundles of conformal blocks for $s{p}_{2\mathrm{\ell }}$ at level one on ${\bar{M}}_{0,n}$. We show their first Chern classes are equivalent to conformal blocks divisors for $s{l}_2$ at level $\mathrm{\ell }$ if and only if the corresponding vector bundles have rank one or zero, and all become equal when the Lie algebra $\mathrm{\ell }$ is large enough. As a consequence of these results, we conclude the cone generated by these divisors is polyhedral.