Irreducibility conjecture for associated varieties of quasi-lisse conical vertex algebras

A quasi-lisse conical vertex algebra is a conical vertex algebra whose associated variety is a zero-dimensional symplectic-leaf variety. The associated variety is the Poisson variety attached to a vertex algebra through its Zhu-type commutative quotient.

Irreducibility conjecture. The associated variety of a quasi-lisse conical vertex algebra is irreducible.

All examples discussed in the survey have irreducible associated varieties, but the classification of quasi-lisse affine vertex algebras is open in higher rank, so the general assertion remains unproved.