International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 16186, 9 pages
Research Article

The Interplay between Linear Representations of the Braid Group

Mohammad N. Abdulrahim and Nibal H. Kassem

Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut 11072809, Lebanon

Received 19 May 2007; Accepted 10 July 2007

Academic Editor: Howard E. Bell

Copyright © 2007 Mohammad N. Abdulrahim and Nibal H. Kassem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider Wada's representation as a twisted version of the standard action of the braid group, Bn, on the free group with n generators. Constructing a free group, Gnm, of rank nm, we compose Cohen's map BnBnm and the embedding BnmAut(Gnm) via Wada's map. We prove that the composition factors of the obtained representation are one copy of Burau representation and m1 copies of the standard representation after changing the parameter t to tk in the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group.