在素特征域上,Cartan型李超代数是一类重要的有限维单李超代数.本项目拟通过诱导模的方法,利用奇反射、Frobenius理论以及R-形式等工具,在特征大于2的代数闭域上来研究Cartan 型限制李超代数的非限制模表示, 重点研究高度为1的特征标.具体来说,我们主要研究以下三个方面：（1）Cartan型李超代数H(n)和K(n)在特征标高度为1时的不可约表示；（2）Cartan型李超代数W(n),S(n),H(n),K(n)所对应的既约包络代数的Cartan不变量以及Block划分问题；（3）Cartan 型限制李超代数 W(m,n,1),S(m,n,1),H(m,m,1),K(m,n,1)在特征标高度为1时的非限制表示.本项目的结果将会充实李超代数的模表示理论.

Lie superalgebras of Cartan type is one of the important kinds of finite dimensional simple Lie superalgebras in prime characteristic.Through the methods of induced modules、odd reflection、Frobenius theory and R-form, we plan to study the non-restricted representations of the restricted Lie superalgebras of Cartan type over an algebraically closed field of characteristic p>2. We focus on the case when the height of the character equals to one. Specifically, we will mainly study the following three questions:(1)The irreducible representations of H(n) and K(n) with p-chanacter of height one;(2)For the reduced enveloping superalgebras of W(n),S(n),H(n),K(n), we will study the Cartan invariants and the partition of Blocks of the reduced enveloping superalgebras;(3) The irreducible non-restricted representations of W(m,n,1),S(m,n,1),H(m,m,1),K(m,n,1) with p-chanacter of height one. The result of this project will enrich the modular representation theory of Lie superalgebras.