Associated varieties of simple affine VOAs $L_k(s{l}_3)$ and $W$-algebras $W_k(s{l}_3,f)$

Cuipo Jiang, Jingtian Song

In this paper we first prove that the maximal ideal of the universal affine vertex operator algebra $V^k(s{l}_n)$ for $k=-n+\frac{n-1}{q}$ is generated by two singular vectors of con…