Alina Marian

The level-rank duality for nonabelian theta functions.

Abstract: Spaces of sections of tensor powers of the theta line bundle on moduli spaces of semistable arbitrary rank bundles on a smooth curve are subject to a level-rank duality: each space of sections is geometrically isomorphic to the dual of the space of sections obtained by interchanging the tensor power (level) of the theta bundle on the moduli space and the rank of the bundles that make up the moduli space. I will describe a proof of this duality, which is the result of joint work with Dragos Oprea, and draws inspiration from work by Prakash Belkale who established the isomorphism for a generic curve.