本项目主要研究与量子群表示理论密切相关的一些有限维、无限维结合代数的表示理论，具体包括：(1)研究量子 walled Brauer 代数的仿射化;(2)研究仿射量子walled Brauer 代数的表示理论;(3)研究分圆量子walled Brauer 代数与量子一般线性(超)群之间的 Schur-Weyl 对偶;(4)研究分圆 Birman-Murakami-Wenzl 代数与量子辛群、正交群之间的 Schur-Weyl 对偶。这些问题及其相关课题的研究对量子群的表示理论的研究具有重要意义。

In this project, we will focus on the representations of some finite and infinite associative algebras which are closely related to the representations of quantum groups, including the following issues. The first one is about the affinization of the quantized walled Brauer algebras; The second one is about the representations of affine quantized walled Brauer algebras; The third one is about the Schur-Weyl duality between the cyclotomic quantized walled Brauer algebras and quantum general linear (super)groups; The fourth one is about the Schur-Weyl duality between cyclotomic Birman-Murakami-Wenzl algebras and quantum orthogonal、symplectic groups. The study of these problems will play an important role in the representations of quantum groups.