Finite-generation conjecture for conformal blocks of simple Lie algebras

Let $\mathfrak{g}$ be a simple Lie algebra, and let $X$ be a stable curve in $\overline{\mathcal{M}}_{g,n}$. Write $\mathbb{V}_{X,\mathfrak{g}}^{\dagger}$ for the algebra of conformal blocks associated with $X$ and $\mathfrak{g}$. Finite-generation conjecture. For every such $X$ and $\mathfrak{g}$, the algebra

$$\mathbb{V}_{X,\mathfrak{g}}^{\dagger}$$

is finitely generated. This proposes extending the paper's finite-generation result to conformal blocks for arbitrary simple Lie algebras; the surrounding text notes that the generalization beyond type $A$ is left for future work.