Classification of quasi-lisse simple affine vertex algebras

We classify all noncritical levels k for which the simple affine vertex algebra Lₖ(g) is quasi-lisse, for every finite-dimensional complex simple Lie algebra g. We prove that Fiebig's equivalence between the corresponding noncritical blocks of category O identifies the relevant parabolic Wakimoto modules and the homomorphisms from the corresponding universal affine vertex algebras. Combining this compatibility with a characterization of semisimple points in associated varieties, we establish that for coprime positive integers $p,q$, L-h⁺p/q(g) is quasi-lisse if and only if L-h⁺p/(q,r)(g) is quasi-lisse, where r is the lacing number of g. The classification at the resulting levels is obtained using Drinfeld--Sokolov reduction, singular vectors and relations in the reductions of the maximal ideals of Vᵏ(g). We also determine the associated varieties at the quasi-lisse levels for all g of rank at most six and for E₇ and E₈.