本项目主要研究几类重要的量子代数的表示。研究内容主要集中在：考虑量子仿射代数表示的张量积的模结构，并构造其R-矩阵；同时还将刻画量子Toroidal代数的结构和表示理论。这些研究课题是代数方向的主流和热门的研究方向，是当前本领域中非常有意义和具有挑战性的研究课题。在本项目执行期间，将围绕本项目中的关键问题，邀请国内外本领域的4位国际前沿专家进行专题报告，集中开展定期的研讨活动，加深对量子代数表示理论的理解，旨在解决量子代数表示理论中几个关键问题，促进量子代数表示理论的研究。

In this project, we will mainly study the representation of several important quantum algebras. The research mainly focuses on: considering the module structures of tensor product of the representations of quantum affine algebras, and construct its R- matrix; describing the structures and representations of quantum toroidal algebra. These research topics are in the essential and popular research algebra field, which are the meaningful and challenging research problems in this field. During the implementation of this project, we will invite four outstanding experts of this field to make a series special topic talks, focusing on the key problems of the project, and concentrate on regular research seminars and activities to have better understanding the representation theory of the quantum algebras， in order to solve some key problems in the theory of quantum algebra, and to promote the research the representation theory of quantum algebra.