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We consider Krammer's representation of the pure braid group on three strings: 3→(3,[±1,±1]), where  and  are indeterminates. As it was done in the case of the braid group, 3, 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, 3

Krammer's Representation of the Pure Braid Group,