Coxeter Covers of the Classical Coxeter Groups

Let C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY (T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), CY (T) is a generalized Coxeter group, too . Let At,n be a group which contains t Abelian groups generated by n elements. The main result in this paper is that CY (T) is isomorphic to At,n Bn or At,n Dn, depends on whether the signed graph T contains loops or not, or in other words C(T) is simply-laced or not, and t is the number of the cycles in T. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups.

• Type: Journal
• Year: 2010
• Where: IJAC
• Authors: Meirav Amram, Robert Shwartz, Mina Teicher
• Keywords: Classical Coxeter Groups, Coxeter Groups, Generalized Coxeter Groups, IJAC 2010