Resumen de Orthosymplectic Feigin–Semikhatov duality

Justine Fasquel, Shigenori Nakatsuka

• We study the representation theory of the subregular W-algebra Wk (so2n+1, fsub) of type B and the principal W-superalgebra W(osp2|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 Wk (so2n+1, fsub) and W(osp2|2n) and derive the character formulae