The universal N=2 supersymmetric W_infty algebra exists as a 2-parameter family whose Y-algebra quotients satisfy the conjectured dualities, giving coset realizations and strong rationality for W_k(sl_{n+1|n}) at k = -1 + 1/(n+a+1).
Gannon,Exotic quantum subgroups and extensions of affine Lie algebra VOAs – part I, [arXiv:2301.07287 [math.QA]]
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Universal $2$-parameter $\mathcal{N}=2$ supersymmetric $\mathcal{W}_{\infty}$-algebra
The universal N=2 supersymmetric W_infty algebra exists as a 2-parameter family whose Y-algebra quotients satisfy the conjectured dualities, giving coset realizations and strong rationality for W_k(sl_{n+1|n}) at k = -1 + 1/(n+a+1).