Strange Duality of Verlinde spaces for G_2 and F_4

TL;DR

This paper establishes a strange duality between Verlinde spaces for G_2 and F_4 at level one on smooth curves, using theta divisors and conformal blocks, with implications for algebraic geometry.

Contribution

It proves a new strange duality for G_2 and F_4 Verlinde spaces at level one, including a parabolic generalization and divisor identities in moduli spaces.

Findings

Strange duality between G_2 and F_4 Verlinde spaces proven.

Parabolic generalization in terms of conformal blocks established.

Identities between conformal blocks divisors in Picard group derived.

Abstract

We prove that the pull back of the canonical theta divisor for E_8-bundles at level one induces a strange duality between Verlinde spaces for G_2 and F_4 at level one on smooth curves of genus g. We also prove a parabolic generalization in terms of conformal blocks and write down identities between conformal blocks divisors in the Picard group of \bar-M_{g,n}.