中科院数学与系统科学研究院
数学研究所
学术报告
表示论研讨班
报告人： 傅翔 教授（北京大学）
题 目：REFLECTION SUBGROUPS OF COXETER GROUPS（I）
时 间：2022.10.13（星期四）14:30-15:30
地 点：数学院南楼N803
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题 目：REFLECTION SUBGROUPS OF COXETER GROUPS（II）
时 间：2022.10.20（星期四）14:30-15:30
地 点：数学院南楼N803
摘 要：Coxeter groups and reflection groups are important mathematical objects arising in a multitude of mathematical and physical contexts, ranging from Lie theory, represen-tation theory to combinatorial and geometric group theory and beyond. The former are essentially abstract combinatorial objects and the latter are groups acting on concrete vector spaces with specific geometric properties. These two types of groups are often studied in conjunction under the celebrated Tits realization, and their boundaries are often obscured even to the experts. Surprising as it might sound, they are ultimately distinct objects with the possibility of the same Coxeter group admitting different Tits realizations and giving rise to different reflection groups exhibiting varying geometric and topological properties. Such subtleties are made more complicated when it comes down to the reflection subgroups of these two types of groups, especially to the construction of root subsystems. Unlike in the classical Lie theory, the notion of a root subsystem might carry ambiguity and uncertainty in general infinite Coxeter groups and reflection groups. In a series of two talks, we wish to present an intentionally indeterministic picture of general infinite Coxeter groups, reflection groups and their reflection subgroups. These talk are based on recent joint works with Lawrence Reeves of Melbourne University and Xu Linxiao of Xi’an Jiaotong-Liverpool University.
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