  We employ appropriate realizations of the affine Hecke algebra and we recover
previously known non-diagonal solutions of the reflection equation for the
$U_{q}(\hat{gl_n})$ case. With the help of linear intertwining relations
involving the aforementioned solutions of the reflection equation, the symmetry
of the open spin chain with a particular choice of the left boundary is
exhibited. The symmetry of the corresponding local Hamiltonian is also
explored.
