Vanishing and identities of conformal blocks divisors

TL;DR

This paper explores symmetries and vanishing properties of conformal block divisors on moduli spaces, revealing new symmetries and their relation to quantum cohomology of Grassmannians.

Contribution

It uncovers new symmetries of conformal block divisors under level and rank interchange and establishes their vanishing above the critical level.

Findings

Conformal block divisors exhibit new symmetries under non-standard level and rank interchange.

Divisors vanish above the critical level, linking to quantum cohomology of Grassmannians.

Provides insights into the structure of moduli spaces and conformal blocks.

Abstract

Conformal block divisors in type A on $\bar{M}_{0,{n}}$ are shown to satisfy new symmetries when levels and ranks are interchanged in non-standard ways. A connection with the quantum cohomology of Grassmannians reveals that these divisors vanish above the critical level.