Fusion and Analytical Bethe Ansatz for the $A_{\text{n}-1}^{(1)}$ Open Spin Chain

We generalise the fusion procedure for the $A_{\text{n}-1}^{(1)}$ open spin chain ($\text{n}>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\text{n}-1}^{(1)}$ open spin chain with $U_{q} (SU(\n))$ symmetry by means of the analytical Bethe ansatz method. Our results coincide with the known ones obtained by means of the nested Bethe ansatz.