2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185466We generalise the fusion procedure for the $A_{\n-1}^{(1)}$ open spin chain ($\n>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\n-1}^{(1)}$ 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.14 pages, LaTeXHigh Energy Physics - Theorytext