The Prym-Hitchin Connection and Anti-Invariant Level-Rank Duality

TL;DR

This paper constructs a Hitchin-type connection on non-abelian theta functions over Prym varieties, demonstrating a level-rank duality that respects flat connections across levels, advancing understanding of geometric dualities in algebraic geometry.

Contribution

It introduces a new Hitchin-type connection on Prym varieties and establishes a level-rank duality that is compatible with flat connections at all levels.

Findings

Duality holds for level one

Duality respects flat connections at all levels

Constructs a Hitchin-type connection on Prym varieties

Abstract

We construct a "Hitchin-type" connection on bundles of non-abelian theta functions on higher-rank Prym varieties, for unramified double covers of curves. We formulate a version of level-rank duality in this Prym setting (building on work of Zelaci), show it holds for level one, and establish that the duality respects the flat connections at all levels.