Classification conjecture for fermion representations of affine Krichever–Novikov algebras

Let $\Sigma$ be the underlying compact Riemann surface of genus $g$, let $\mathfrak{g}$ be the finite-dimensional Lie algebra used to construct the affine Krichever–Novikov algebra $\hat{\mathfrak{g}}$, and let $r$ and $l$ denote the rank and representation dimension occurring in the construction. A fermion representation is the representation obtained from the fermionic Fock-space construction described above. Classification conjecture. The equivalence classes of fermion representations of $\hat{\mathfrak{g}}$ are in one-to-one correspondence with the following pairs: an equivalence class of a holomorphic bundle of rank $r$ and degree $gr$ on $\Sigma$ and an equivalence class of an $l$-dimensional representation of the algebra $\mathfrak{g}$. This proposes a geometric and finite-dimensional parametrization of the fermion representations; the supplied text does not state whether the correspondence has been proved or disproved.