Krammer′s Representation of the Pure Braid Group, P3
Mohammad N. Abdulrahim, M. Al Tahan · International Journal of Mathematics and Mathematical Sciences · 2010
We consider Krammer′s representation of the pure braid group on three strings: P3 → GL(3, Z[t±1, q±1]), where t and q are indeterminates. As it was done in the case of the braid group, B3, we specialize the indeterminates t and q 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, P3.