Integrability of Open Spin Chains with Quantum Algebra Symmetry

in the fundamental representation. Conspicuously absent from this list is A (1) n for n > 1. This is because in order to demonstrate integrability, we assume that the corresponding R matrix has crossing symmetry, which is not true in the case A (1) n for n > 1. Sklyanin has demonstrated that an integrable open spin chain can be constructed with an R matrix that satisfies nothing more than the Yang-Baxter equation. In particular, no assumption of crossing symmetry is necessary. This suggests that the quantum-algebrainvariant open chain associated with A (1) n for n > 1 may be integrable. In this Addendum, we show that this is in fact the case. Let R(u) be a solution of the Yang-Baxter equation corresponding to a non-exceptional affine Lie algebra g in the fundamental representation. According to Bazhanov and Jimbo, such an R matrix has PT symmetry P12 R12(u) P12 ≡ R21(u) = R12(u) t1t2 , (1)