  We consider integrable open spin chains related to the quantum affine
algebras U_q(o(3)) and U_q(A_2^{(2)}). We discuss the symmetry algebras of
these chains with the local C^3 space related to the Birman-Wenzl-Murakami
algebra. The symmetry algebra and the Birman-Wenzl-Murakami algebra centralize
each other in the representation space, and this defines the structure of the
spin system spectra. Consequently, the corresponding multiplet structure of the
energy spectra is obtained.
