Reading Seminar on Coxeter Groups


Venue/Location: C101, VIASM

Speaker: Le Thanh Hoang (VNU-HUS)

Link Zoom:
Meeting ID: 958 0796 8618
Passcode: 925672


In the last seminar talk, I stated and proved Matsumoto's exchange condition, which is an important property of Coxeter groups. In the next talk, I will recall Matsumoto's exchange condition, and prove that this is a sufficient condition for a group to be a Coxeter group. After that, I will introduce the notion of crystallographic Coxeter groups; using combinatorial methods, I will prove the Classification Theorem of Finite Crystallographic Coxeter groups (Hiller's book, chapter 1, section 4). In particular, the finite crystallographic Coxeter groups are classified up to isomorphism by their Coxeter graphs, and we can explicitly describe the class of all Coxeter graphs of finite crystallographic Coxeter groups.