本项目主要研究李超代数（包括仿射李超代数）以及current共形李超代数的表示中的一些问题，如仿射李超代数的Verma模结构以及Jantzen滤过；不可约模的特征标公式以及Kazhdan-Lusztig理论；上同调理论；模范畴的性质；建立可能的Schur-Weyl对偶理论等。同时研究与（仿射）李超代数密切相关的current共形超代数、量子超群、超Yangians等一些超代数的表示。

In this proposal, we work on several problems related to representations of Lie superalgebras (including affine Lie superalgebras) and current conformal Lie superalgebras, for example, structures of Verma modules of affine Lie superalgebras and Jantzen filtrations of Verma modules; character formulas for irreducible modules and Kazhdan-Lusztig theory; cohomology theory; properties of module categories; establishing possible Schur-Weyl dualities; etc. We also study representations of some super algebras related to (affine) Lie superalgebras such as current conformal Lie superalgebras, quantum supergroups and super-Yangians.