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We consider a 2-dimensional representation of the Hecke algebra$\mathcal{H}(G_7, u)$, where $G_7$ is the complex reflection group and $u$ isthe set of indeterminates $u=(x_1, x_2, y_1, y_2, y_3, z_1, z_2, z_3)$. Afterspecializing the indetrminates to non zero complex numbers, we then determine anecessary and sufficient condition that guarantees the irreducibility of thecomplex specialization of the representation of the Hecke algebra $H(G_7, u)$.

On the Irreducibility of the Complex Specialization of the Representation of The Hecke Algebra of the Complex Reflection Group $G_7$