The Interplay between Linear Representations of the Braid Group

Mohammad N. Abdulrahim and Nibal H. Kassem

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-9

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:016186

DOI: 10.1155/2007/16186

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