Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory

The algebraic structure and the spectral properties of a special class of multicomponent NLS equations, related to the symmetric spaces of 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 g. Special attention is paid to the structure of the dressing factors in spinor representation of the orthogonal simple Lie algebras of Br ≃ so(2r + 1,C) type.