Rank-level duality of conformal blocks of GL_n and SL_n

TL;DR

This paper extends the proof of rank-level duality for conformal blocks from non-abelian theta functions to sections over moduli spaces of parabolic vector bundles, also linking dualities between symplectic groups.

Contribution

It generalizes Marian and Oprea's proof to a broader setting involving parabolic bundles and establishes duality between Sp(2) and Sp(2n) conformal blocks.

Findings

Extended rank-level duality proof to parabolic vector bundles

Established duality between Sp(2) and Sp(2n) conformal blocks

Connected dualities across different Lie groups

Abstract

We generalise the proof by Marian and Oprea of rank-level duality for non-abelian theta functions to the case of sections of line bundles (conformal blocks) over moduli spaces of parabolic vector bundles over a projective smooth curve. We also describe how it implies the rank-level duality between conformal blocks of Sp(2) and Sp(2n).