Smooth modules of the super \(\mathcal{W}\)-algebra \(\mathcal{SW}(\frac{3}{2}, \frac{3}{2})\) of Neveu-Schwarz type (Q6632109)

The super \(W\)-algebra \(SW(\frac{3}{2},\frac{3}{2})\) (see [\textit{J. M. Figueroa-O'Farrill} and \textit{S. Schrans}, Int. J. Mod. Phys. A 7, No. 3, 591--617 (1992; Zbl 0801.17032)]) is a supersymmetric conformal algebra that incorporates an additional covariant supersymmetric field \(\Phi\) of dimension \((\frac{3}{2},2)\).\N\NIn the paper underestablish a connection between simple smooth modules over \(L\) and simple modules over specific finite-dimensional solvable Lie superalgebras. This relation is used to study smooth modules over the considered super \(W\)-algebras. In particular several examples including simple Whittaker modules and highest weight modules are given.