Symmetries of spin systems and Birman–Wenzl–Murakami algebra

Abstract

We consider integrable open spin chains related to the quantum affine algebras Uq(o(3)ˆ) and Uq(A2(2)). We discuss the symmetry algebras of these chains with the local C3 space related to the Birman–Wenzl–Murakami algebra. The symmetry algebra and the Birman–Wenzl–Murakami algebra centralize each other in the representation space H=⊗1NC3 of the system, and this determines the structure of the spin system spectra. Consequently, the corresponding multiplet structure of the energy spectra is obtained.