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Consider a representation ρ : B3 → GL6(C) constructed by M. Al-Tahan and M. Abdulrahim. We construct a representation φ equivalent to the restriction of ρ on P3 and show that φ is a direct sum of irreducible subrepresentations, which are not equivalent to the reduced Burau representation restricted to P3. Also, we show that the subrepresentations of φ are unitary relative to unique invertible hermitian matrices.

ON THE IRREDUCIBLITY OF THE REPRESENTATION OF THE PURE BRAID GROUP ON THREE STRANDS