Representation Of Special Modular Lie Superalgebra

In this paper,we study the generalized-reduced Kac modules with characteristic height no more than 1 for Special superalgebra S(n)over an algebraic closed field with characteristic p > 3.First,the generalized restriction structure of S(n)is given so that it becomes a generalized restricted Lie superalgebra.Second,we give the necessary and su cient conditions for the generalized-reduced Kac modules with characteristic height no more than 1 for S(n)to be simple,and give the classification and dimension of the isomorphism classes of generalized-reduced simple modules.Finally,as an application,the basis and dimension of the 0-th and 1-th cohomology of S(2)with coe cients in the generalized restricted Kac module with weight 0 are calculated by reduction Lemma.