吴文俊数学重点实验室代数学系列讲座之五十八【Dr. Xiang Fu】
 
报告题目：On infinite Coxeter groups: dominance partial ordering and the distribution of root

报告人：Dr. Xiang Fu

      Peking University

时  间：2014年7月15日（周二）  下午3:00-4:00

地  点：东区管理科研楼  365英国上市官网1518室

内容提要：

In this talk we present a number of new findings concerning a partial ordering defined on root systems of Coxeter groups, called dominance. Dominance was first introduced by Brink and Howlett to prove that there is a finite state automaton capable of recognizing whether two expressions (over Coxeter generators) represented the same group element. Dominance has since been non-trivially utilized in more general combinatorial and algebraic investigations of Coxeter groups. Despite its usefulness, only the dominance-minimal roots were satisfactorily investigated in the literature, and in this talk we describe the behaviour of dominance beyond such minimal roots. Furthermore, we give application of dominance to the geometric representation theory of general infinite Coxeter groups. In particular, we outline our recent joint work with Lawrence Reeves on how dominance can be employed to better understand the distribution of roots in root systems of infinite Coxeter groups.

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