  In this paper we consider two a priori very different problems: construction
of the eigenstates of the spin chains with non parallel boundary magnetic
fields and computation of the partition function for the trigonometric
solid-on-solid (SOS) model with one reflecting end and domain wall boundary
conditions. We show that these two problems are related through a gauge
transformation (so-called vertex-face transformation) and can be solved using
the same dynamical reflection algebras.
