Tuba’s Representation of the Pure Braid Group on Three Strands

We consider Tuba’s representation of the pure braid group, P3, defined by the map Ψ: P3 → GL(V ), where V is an algebraically closed field. We then specialize the indeterminates used in defining the representation to non- zero complex numbers. Our objective is to find necessary and sufficient conditions that guarantee the irreducibility of Tuba’s representations of the pure braid group P3 with dimensions d = 2 and d = 3.