Abstract
The nature ofℓ 5 spin algebra is considered together withℓ 5↓ℓ 5↓C 4v mapping in order to specify the dual spin symmetry for MQ-NMR ofnido-11B5H9. The forms of Gel'fand shapes forℓ 5 spin symmetry are presented to show how they specify thefull range of multiplicities found in higher-n ℓ n -partitions. Tuples, or number-partitions and theirℓ n ↓G invariance sets provide models for both the five-foldI i =3/2 component, and the two distinct types of spin-1/2 subsystems. The full spin symmetry is derived in terms of the direct product ((ℓ 5↓C 4v )⊗(ℓ 4↓C 4v ))1/2⊗(ℓ 5↓C 4v )3/2. The concepts used are implicit in the substructure ofp-tuple model invariances over the subduced symmetry, or derive from the inner tensor product algebras under theℓ n group. Both as a check on the combinatorially derived multiplicities of [λ]s and for insight into (non-simply-reducible) substructure of number-partitions, the study of mapping from :hrr'.:-tuples onto theℓ n -partitional set for higherI i is invaluable. The motivation for this work lies in its pertinence to the MQ-NMR spin dynamics of clusterlike molecules. The accessible information content of a spin algebra over either form of spin space is bound up with a suitable symmetry partitioning of the problem, as implied by the use of {T kq(v:[λ])} bases within higherq subspaces of the Liouville formalism.
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