The infinite-coupling affine vertex operator superalgebra extension conjecture

Let $\mathfrak{g}$ be a reductive simply-laced Lie algebra, let $n$ be a positive integer, and let $P^+_n$ be the set of dominant integral weights of $\mathfrak{g}$ such that $n(\lambda,\lambda)\in\mathbb Z$. Let $R_\lambda$ be the finite-dimensional representation of $\mathfrak{g}$ of weight $\lambda$, and let $M_{n^{-1},\lambda}$ be the corresponding Weyl module for $V_{n^{-1}-h}(\mathfrak{g})$. Infinite-coupling extension conjecture. The module

$$\mathfrak{A}^{(n)}[\mathfrak{g},\infty]=\bigoplus_{\lambda\in P^+_n}R_\lambda\otimes M_{n^{-1},\lambda}$$

for $\mathfrak{g}\otimes V_{n^{-1}-h}(\mathfrak{g})$ can be given the structure of a simple vertex operator superalgebra. In the cases $\mathfrak{g}=\mathfrak{sl}(2)$ and $n=1,2$, the resulting algebras are identified with known coset and small $N=4$ algebras; the general construction remains conjectural.