Root Category and Simple Groups of Lie Type
数学专题报告
报告题目(Title)：Root Category and Simple Groups of Lie Type
报告人(Speaker)：李不言（清华大学）
地点(Place)：后主楼1220
时间(Time)：2025年12月10日（周三）16:00-16:50
邀请人(Inviter)：肖杰、覃帆、周宇
报告摘要
Ringel used the representation theory of finite-type hereditary algebra and Hall polynomials to obtain the positive part of the simple Lie algebra. Peng and Xiao generalized Ringel's result to root category and obtained the whole Lie algebra. Based on their constructions, we construct the compact real form of the complex semisimple Lie algebra, and the Chevalley group of the root category, as well as its maximal compact subgroup. On the other hand, Lusztig used the modified quantum group and its canonical basis to obtain the reductive group and its coordinate ring O, in particular the tensor product decomposition of O. By combining these two kinds of structures, we explore how the classical theory of compact Lie groups, such as Peter-Weyl theorem and Plancherel theorem, can be recovered completely.
