Strange Duality for Verlinde Spaces of Exceptional Groups at Level One

The moduli stack $\mathcal M_X(E_8)$ of principal E8-bundles over a smooth projective curve X carries a natural divisor Δ. We study the pullback of the divisor Δ to the moduli stack $\mathcal M_X(P)$, where P is a semisimple and simply connected group such that its Lie algebra Lie (P) is a maximal conformal subalgebra of Lie (E8). We show that the divisor Δ 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), E6), and (SL (2), E7).