A Note on Restricted Representations of the Witt Superalgebras

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.