Krammer's Representation of the Pure Braid Group, P3

الملخص EN

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.