Dipartimento di Scienze di Base e Applicate per l'Ingegneria

On a class of representations of right-angled Coxeter groups

 

Abstract:

We define an action of any right-angled Coxeter group (these groups are also known as "graph groups") on any Coxeter group, whenever is satisfied a condition of universality of a graph constructed with the Coxeter graph of the group on which we want to act. When the graph of the right-angled Coxeter group is a forest with n vertices, and the group on which we want to act is the symmetric group of order n!, the problem of existence of such representations is solved constructively. For generic graphs the existence is conjecturally true.