Irreducibility of some tensor product of Albeverio's representations of the Braid groups B3 and B4

We consider Albeverio's linear representations of the braid groups B3 and B4. We specialize the indeterminates used in dening these representations to non zero complex numbers. We then consider the tensor products of the representations of B3 and the tensor products of those of B4. We then determine necessary and sucient conditions that guaran- tee the irreducibility of the tensor products of the representations of B3. As for the tensor products of the representations of B4, we only nd sucient conditions for the irreducibility of the tensor product.