We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where$G_7$ is the complex reflection group and $u$ is the set of indeterminates$u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$.After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specializationof the representation of the Hecke algebra $H(G_7, u)$. تفاصيل المقالة

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of the tensor products of the representations of $B_3$‎. ‎As for the tensor products of the representations of $B_4$‎, ‎we only find sufficient conditions for the irreducibility of the tensor product‎. تفاصيل المقالة