Vertex tensor and ribbon category conjecture for admissible affine Lie algebra weight modules

Let $ell$ be an admissible level for the simple Lie algebra $\bf g$. Vertex tensor and ribbon category conjecture.

1. $L_{ell}(\bf g)\operatorname{-wtmod}$ is a vertex tensor category.
2. $L_{ell}(\bf g)\operatorname{-wtmod}$ is a ribbon category.

The paper proves the corresponding vertex tensor category result for $\mathfrak{sl}_2$ and discusses ribbon-category cases, while the stated generalization is presented as expected and remains open.