International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 8, Pages 1321-1326
doi:10.1155/IJMMS.2005.1321
Generalizations of the standard Artin representation are unitary
Department of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut 1107 2809, Lebanon
Received 27 October 2004; Revised 24 February 2005
Copyright © 2005 Mohammad N. Abdulrahim. 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 the Magnus representation of the image of the braid group under the generalizations of the standard Artin representation discovered by M. Wada. We show that the images of the generators of the braid group under the Magnus representation are unitary relative to a Hermitian matrix. As a special case,
we get that the Burau representation is unitary, which was known and proved by C. C. Squier.