At the critical level the centerless subregular W-algebra equals an orbifold of the large-level principal W-superalgebra of sl_{n|1} times a lattice VOA, inducing block-wise equivalences of module categories.
Li, The physics superselection principle in vertex operator algebra theory, Journal of Algebra, 1997, 196(2): 436-457
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Feigin-Semikhatov duality at the critical level
At the critical level the centerless subregular W-algebra equals an orbifold of the large-level principal W-superalgebra of sl_{n|1} times a lattice VOA, inducing block-wise equivalences of module categories.