A Note on Restricted Representations of
the Witt Superalgebras |
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| Authors: | Yufeng YAO and Bin SHU |
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| Affiliation: | 1. Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, China
2. Department of Mathematics, East China Normal University, Shanghai, 200241, China
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| Abstract: | Let F be an algebraically closed field of prime characteristic p > 3, and W (n) the Witt superalgebra over F, which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates. The dimensions of simple atypical modules in the restricted supermodule category for W (n) are precisely calculated in this paper, and thereby the dimensions of all simple modules can be precisely given. Moreover, the restricted supermodule category for W (n) is proved to have one block. |
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| Keywords: | Restricted Lie superalgebra Witt superalgebra Restricted representation Atypical weight |
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