Rank-level duality of Conformal Blocks for odd orthogonal Lie algebras in genus 0

TL;DR

This paper proves a rank-level duality for conformal blocks associated with odd orthogonal Lie algebras on genus 0 curves, confirming a conjecture by Nakanishi and Tsuchiya, and deepening understanding of invariants in algebraic geometry and mathematical physics.

Contribution

It establishes a new rank-level duality for type so(2r+1) conformal blocks on genus 0, confirming a conjecture and expanding the theory of conformal invariants.

Findings

Proved a conjectured rank-level duality for so(2r+1) conformal blocks.

Connected conformal blocks of different Lie algebras via duality.

Enhanced understanding of invariants in algebraic geometry and physics.

Abstract

Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants known as conformal blocks. Conformal blocks appear in algebraic geometry as spaces of global sections of line bundles on the moduli stack of parabolic bundles on a smooth curve. Rank-level duality connects a conformal block associated to one Lie algebra to a conformal block for a different Lie algebra. In this paper we prove a rank-level duality for type so(2r+1) on the pointed projective line conjectured by T. Nakanishi and A. Tsuchiya.