Diagram automorphisms and Rank-Level duality

Abstract

We study the effect of diagram automorphisms on rank-level duality. We use it to prove new symplectic rank-level dualities on genus zero smooth curves with marked points and chosen coordinates. We also show that rank-level dualities for the pair sl(r), sl(s) in genus 0 arising from representation theory can also be obtained from the parabolic strange duality proved by R. Oudompheng.