李代数在物理学等其它学科中的应用主要通过其表示实现。相对于权表示，非权表示发展缓慢，存在大量问题有待解决。本项目主要研究与（广义） Virasoro 代数相关的无限维李代数的非权表示。研究内容有以下两个方面：（1）将拟-Whittaker 模这一概念由有限维李代数推广到与（广义） Virasoro 代数相关的无限维李代数，完成有关单拟-Whittaker 模的分类；（2）刻画并实现与Virasoro 代数相关的无限维李代数的一类模范畴，其对象限制在 Cartan 子代数（模掉中心）上是有限秩的自由模，进一步地，通过建立此类模范畴与其它模范畴之间的对应关系探究此类模范畴的性质。本项目的研究将对无限维李代数表示理论的建立起到积极的推动作用。

The application of Lie algebra in physics and other disciplines is mainly realized by its representation. Compared with weight module theory, the progress of non-weight module theory is slow, and there are a lot of problems that have to be solved. In this project, we are mainly concerned with the non-weight modules for the algebras related to (generalized) Virasoro algebra. The content of this project can be divided into the following two aspects: (1) We will generalize quasi-Whittaker module for finite-dimensional Lie algebras to infinite-dimensional Lie algebras related to (generalized) Virasoro algebra and give a classification of related simple quasi-Whittaker modules. (2) We will investigate and realized the category consisting of modules which are free of finite rank when restricted to the Cartan subalgebra over infinite-dimensional Lie algebras related to Virasoro algebra. Furthermore, the properties of such module category are characterized by exploring the relationship between this kind of category and others. The content of this project will positively promote the construction of the research system of representations of infinite-dimensional Lie algebras.