本项目主要研究典型李超代数的抛物范畴O中存在的一系列基本而重要的问题：抛物Verma模的Jantzen滤过的 Loewy性，进而确定抛物Verma模的结构并给出不可约模的特征标和维数的Weyl型公式，以及研究抛物范畴O的Kazhdan-Lusztig理论和上同调理论；研究投射模、内射模和tilting模的性质；研究抛物范畴O的一个block的projective generators的自同态代数，进而建立李超代数的抛物范畴O的一个block与一些重要的结合代数的模范畴的等价关系。

In this project, we are mainly concerned with the following fundamental and important problems in parabolic category O of Lie superalgebras: Loewy property of Jantzen filtrations of parabolic Verma modules, and further the determination of structures of parabolic Verma modules and Weyl type formulae of characters and dimensions of irreducible modules, and sdudying the Kazhdan-Luzstig theory and cohomology theory of parabolic category O; studying properties of projective modules, injective modules and tilting modules; studying endomorphism algebras of projective generators of blocks of parabolic category O, and establishing equivalence between blocks of parabolic category O and module categories of some associative algebras.