International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 16186, 9 pages
doi:10.1155/2007/16186
Research Article
The Interplay between Linear Representations of the Braid Group
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.
Abstract
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 Bn→Bnm and the embedding Bnm→Aut(Gnm) via Wada's map. We prove that the composition factors of the obtained
representation are one copy of Burau representation and m−1 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.