Conformal Blocks in type C at level one

Abstract

We investigate the behavior of vector bundles of conformal blocks for $s{p}_{2\ell }$ 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 $\ell$ 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.

24 pages