Orthosymplectic Feigin-Semikhatov duality

We study the representation theory of the subregular W-algebra ${\mathcal{W}}^k({\mathfrak{s}\mathfrak{o}}_{2n+1},f_{sub})$ of type B and the principal W-superalgebra ${\mathcal{W}}^{\mathrm{\ell }}({\mathfrak{o}\mathfrak{s}\mathfrak{p}}_{2\mathrm{\mid }2n})$, which are related by an orthosymplectic analogue of Feigin-Semikhatov duality in type A. We establish a block-wise equivalence of weight modules over the W-superalgebras by using the relative semi-infinite cohomology functor and spectral flow twists, which generalizes the result of Feigin-Semikhatov-Tipunin for the N=2 superconformal algebra. In particular, the correspondence of Wakimoto type free field representations is obtained. When the level of the subregular W-algebra is exceptional, we classify the simple modules over the simple quotients ${\mathcal{W}}_k({\mathfrak{s}\mathfrak{o}}_{2n+1},f_{sub})$ and ${\mathcal{W}}_{\mathrm{\ell }}({\mathfrak{o}\mathfrak{s}\mathfrak{p}}_{2\mathrm{\mid }2n})$ and derive the character formulae.