On the symmetries of integrable systems with boundaries

We employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the $U_q(\widehat{g{l}_n})$ 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.