Principal orthosymplectic W-superalgebra rationality conjecture

Let $n\geq 1$ and set

$$\psi'=\frac{p}{2(p+q)}.$$

Assume that $p,q\in\mathbb N$ are coprime, that $p\geq 2n-1$ when $q$ is odd, and that $p\geq 2n$ when $q$ is even. Principal orthosymplectic W-superalgebra rationality conjecture. The principal W-superalgebra $\mathcal W_{\psi'-n-1/2}(\mathfrak{osp}_{1|2n})$ is lisse and rational. By Feigin–Frenkel duality, the corresponding algebra at $\psi'=1/(4\psi)=(p+q)/(2p)$ is likewise predicted to be lisse and rational. This conjecture is motivated by a diagonal coset realization and analogy with the simply-laced case; its general status is open.