Arakawa–Moreau's irreducibility conjecture for associated varieties of quasi-lisse vertex algebras

Let $V$ be a simple quasi-lisse conformal vertex algebra, and let $X_V$ denote its associated variety. Arakawa–Moreau's conjecture.

$$X_V\text{ is irreducible}.$$

The paper explains that the theorem proved there supplies a new example in which this conjecture holds. The conjecture remains unresolved in general according to the information given in the source.