Quasifinite highest weight modules over the superW1+∞algebra

AbstractWe study quasifinite highest weight modules over the supersymmetric extension of theW1+∞ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by polynomials, and obtain the differential equations for highest weights. The spectral flow, free field realization over the (B, C)-system, and the embedding into $$\widehat{gl}$$ (∞|∞) are also presented.