We consider a 2-dimensional representation of the Hecke algebra  where  is the complex reflection group and u is the set ofindeterminates  Afterspecializing the indeterminates to non-zero complex numbers on the unit circle, we prove that the representation is unitary relative to a Hermitian positive definite matrix. We then determine a necessary and sufficient condition for an element of  to belong to the kernel of the complex specialization of the representation of the Hecke algebra

braid group, Hecke algebra, irreducible, reflections.