The algebraic structure and the spectral properties of a special class of multi-component NLS equations, related to the symmetric spaces of { \bf BD.I}-type are analyzed. The focus of the study is on the spectral theory of the relevant Lax operators for different fundamental representations of the underlying simple Lie algebra $\mathfrak{ g}$. Special attention is paid to the structure of the dressing factors in spinor representation of the orthogonal simple Lie algebras of ${ \bf B}_r\simeq so(2r+1,{ \mathbb C})$ type.
Categories: nlin.SI math-ph math.MP