Rank-Level duality and Conformal Block divisors

Abstract

We describe new relations among conformal block divisors in $\mathrm{Pic}({\bar{M}}_{0,n})$. These relations appear from various rank-level dualities of conformal blocks on ${\mathbb{P}}^1$ with $n$ marked points. We also give a coordinate free description of rank-level duality maps on ${\overline{\mathcal{M}}}_{g,n}$.

arXiv commentProof of conjecture is given and a result about vanishing of conformal blocks divisors is added. To appear in Adv. Math