Rank-zero irregular Neveu-Schwarz vertex operators are shown to exist uniquely, and their decomposition into Virasoro irregular vertex operators yields bilinear operators that coincide with the quantum Painlevé V and IV tau-function equations.
Simple restricted modules for Neveu-Schwarz algebra
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abstract
In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We establish a 1-1 correspondence between simple restricted Neveu-Schwarz modules and simple modules of a family of finite dimensional solvable Lie superalgebras associated to the Neveu-Schwarz algebra. Moreover, for two of these superalgebras all simple modules are classified.
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Neveu--Schwarz Irregular Vertex Operators, Decomposition Theorems, and Bilinear Operators
Rank-zero irregular Neveu-Schwarz vertex operators are shown to exist uniquely, and their decomposition into Virasoro irregular vertex operators yields bilinear operators that coincide with the quantum Painlevé V and IV tau-function equations.