Strange duality for Verlinde spaces of exceptional groups at level one

TL;DR

This paper establishes new 'Strange Duality' isomorphisms between Verlinde spaces at level one for certain pairs of groups related to the exceptional group E_8, revealing deep geometric and algebraic relationships.

Contribution

It demonstrates novel dualities between Verlinde spaces for specific group pairs derived from E_8, expanding understanding of geometric representation theory.

Findings

Isomorphisms between Verlinde spaces for (SL(5), SL(5))

Isomorphisms for (Spin(8), Spin(8))

Isomorphisms for (SL(3), E_6) and (SL(2), E_7)

Abstract

The moduli stack M_X(E_8) of principal E_8-bundles over a smooth projective curve X carries a natural divisor Delta. We study the pull-back of the divisor Delta to the moduli stack M_X(P), where P is a semi-simple and simply connected group such that its Lie algebra Lie(P) is a maximal conformal subalgebra of Lie(E_8). We show that the divisor Delta induces "Strange Duality"-type isomorphisms between the Verlinde spaces at level one of the following pairs of groups (SL(5), SL(5)), (Spin(8), Spin(8)), (SL(3), E_6) and (SL(2), E_7).