  Motivated by earlier works 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. The corresponding $N$
site spin chain with open boundary conditions is then constructed and boundary
non-local charges associated to the non-diagonal solutions of the reflection
equation are derived, as coproduct realizations of the reflection algebra. With
the help of linear intertwining relations involving the aforementioned
solutions of the reflection equation, the symmetry of the open spin chain with
the corresponding boundary conditions is exhibited, being essentially a remnant
of the $U_{q}(\hat{gl_{n}})$ algebra. More specifically, we show that
representations of certain boundary non-local charges commute with the
generators of the affine Hecke algebra and with the local Hamiltonian of the
open spin chain for a particular choice of boundary conditions. Furthermore, we
are able to show that the transfer matrix of the open spin chain commutes with
a certain number of boundary non-local charges, depending on the choice of
boundary conditions.
