INVARIANT SUBALGEBRAS OF THE SMALL

Various aspects of orbifolds and cosets the small $\mathcal{N}=4$ superconformal algebra are studied. First, we determine minimal strong generators for generic specific levels. As a corollary, obtain vertex global sections chiral de Rham complex on any Enriques surface. We also identify with $\text{Com}(V^{\ell}(\mathfrak{sl}_2), V^{\ell+1}(\mathfrak{sl}_2) \otimes \mathcal{W}_{-5/2}(\mathfrak{sl}_4, f_{\text{rect}}))$ in addition at special levels Grassmanian principal $\mathcal{W}$-algebras type $A$ degenerate admissible These coincidences lead us to novel level-rank duality involving Grassmannian supercosets.