Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut 1107 2809, Lebanon
Copyright © 2010 Mohammad N. Abdulrahim and Madline Al-Tahan. 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 Krammer's representation of the pure braid group on three strings: , where and are indeterminates. As it was done in the case of the braid group, , we specialize the indeterminates and to nonzero complex numbers. Then we present our main theorem that gives us a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of Krammer's representation of the pure braid group, .