Representations Of The Cartan Lie Superalgebras Of The Witt And Special Type

Let k be an algebraically closed field of characteristic p> 2 throughout this paper and g stands for W(n) or S(n). which are the Witt superalgebra or the Special superalgebra of Cartan type respectively. When refere to S(n). we assume that p(?)n in addition.This paper is divided into three parts. In the first two parts, we study the non-restricted irreducible representation of g with p-character of height one. The follow-ing results are given:Firstly, any irreducible Ux(g)-module is a simple quotient of the Kac-module. Then, the necessary and sufficient condition when Kac-module is irreducible is given. Furthermore, when the Kac-module is reducible, composition factors of Kac-module and the multiplicities are comfirmed. Finally, the dimension of the simple modules can be given.In the third part, Cartan invariants of Ux(W(2)) are given for any p-character x up to isomorphism.