Abstract
The multipole formulation of N.M.R., as applied to multi-spin systems, makes use of a basis that is composed of rotationally invariant tensor operators. For spin systems that have magnetic symmetry, it is possible to adapt this Liouville space into a basis which is also irreducible under the appropriate permutation symmetry. This permits a systematic treatment of the various multiquantum spectra and leads to a dramatic factorization of the Liouville matrix. Examples of AA′ and AA′BB′ ≡ [AB]2 systems are included as illustrations. The effect of introducing the weak coupling limit is shown to further reduce the dimensionality of submatrices for the related [AX]2 system.