The Interplay between Linear Representations of the Braid Group. (29th August 2007)

• Record Type: Journal Article
• Authors: Abdulrahim, Mohammad N.; Kassem, Nibal H.
• Other Names: Bell Howard E. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Voume 2007(2007)
• Publication Date: 2007-08-29
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2007/16186
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : We consider Wada's representation as a twisted version of the standard action of the braid group, B n, on the free group with n generators. Constructing a free group, G n m, of rank n m, we compose Cohen's map B n → B n m and the embedding B n m → Aut ( G n m ) 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 t k 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.