Abstract
In this paper, we explore the super W-algebra SW(32,32) of Neveu-Schwarz type denoted by L, which serves as a supersymmetric conformal algebra. Our investigation focuses on the analysis of simple smooth modules including the Whittaker modules and the highest weight modules over L. Specifically, we utilize simple modules from finite-dimensional solvable Lie superalgebras to construct a multitude of simple smooth modules over L. Additionally, we provide several equivalent descriptions for simple smooth modules over L.
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