Rank-Level duality and Conformal Block divisors

TL;DR

This paper explores new relationships among conformal block divisors on moduli spaces of curves, revealing rank-level dualities that deepen understanding of their geometric and algebraic structures.

Contribution

It introduces novel relations among conformal block divisors and provides a coordinate-free description of rank-level duality maps on moduli spaces.

Findings

New relations among conformal block divisors

Coordinate-free description of rank-level duality maps

Insights into the structure of moduli spaces

Abstract

We describe new relations among conformal block divisors in $\operatorname{Pic}(\bar{\operatorname{M}}_{0,n})$. 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 $\overline{\mathcal{M}}_{g,n}$.