Abstract
In this paper, the authors prove that certain quantum spin chains with quantum-algebra symmetry are integrable. Specifically these are the quantum-algebra-invariant open chains associated with the affine Lie algebras A[sub 1][sup (1)], A[sub 2n][sup (2)], A[sub 2n [minus] 1][sup (2)], B[sub n][sup (1)], C[sub n][sup (1)], and D[sub n][sup (1)] in the fundamental representation. Conspicuously absent from this list is A[sub n][sup (1)] for n [gt] 1. This is because in order to demonstrate integrability, the authors assume that the corresponding R matrix has crossing symmetry, which is not true in the case A[sub n][sup (1)] for n [gt] 1.
