Abstract

Riemann’s moduli space of curves can naturally be equipped with a range of bundles, whose fibres are spaces of non-abelian theta functions or, equivalently, spaces of conformal blocks. These bundles come naturally equipped with flat projective connections, in many ways mirroring an old story for (abelian) theta functions, who were classically known to satisfy a heat-equation. In some aspects however the non-abelian theta functions behave quite differently, most clearly exhibited when considering the projective representations of the mapping class group they give rise to. For a few sporadic, low-level versions this difference brakes down though, a phenomenon best understood through strange duality. In this talk we will describe the situation for rank 4, where the situation gets clarified by thinking about higher-rank Prym varieties. This is joint ongoing work with T. Baier, M. Bolognesi and C. Pauly.