  For the classical principal chiral model with boundary, we give the subset of
the Yangian charges which remains conserved under certain integrable boundary
conditions, and extract them from the monodromy matrix. Quantized versions of
these charges are used to deduce the structure of rational solutions of the
reflection equation, analogous to the 'tensor product graph' for solutions of
the Yang-Baxter equation. We give a variety of such solutions, including some
for reflection from non-trivial boundary states, for the SU(N) case, and
confirm these by constructing them by fusion from the basic solutions.
