Strange duality and the Hitchin/WZW connection
arXiv:0705.0717
Abstract
For a compact Riemann surface X of positive genus, the space of sections of certain theta bundle on moduli of bundles of rank r and level k admits a natural map to (the dual of) a similar space of sections of rank k and level r (the strange duality isomorphism). Both sides of the isomorphism carry projective connections as X varies in a family. We prove that this map is (projectively) flat.
The only change made is a clarification of the recent history of the strange duality conjecture