Braid groups and higher representation theory

对称是经典表征理论中的一个核心概念。在高级表征理论中，经典表征理论的对称性被高级对称性所取代。这些更高的对称性包含了在经典水平上不存在的新结构。本研究将在经典表征理论和几何群论的基础上发展基本对象的高级表征理论，重点研究辫状群和量子群。

Symmetry is a central notion in classical representation theory. In higher representation theory the symmetries of classical representation theory are replaced by higher symmetries. These higher symmetries contain new structure not present at the classical level. The proposed research will develop the higher representation theory of fundamental objects from classical representation theory and geometric group theory, focusing on braid groups and quantum groups.