Abstract
The inherent (in)determinacy implicit in the SU(m≥3)×S n↓G natural embedding aspects of (NMR) spin symmetry of clusters is investigated, as part of a multicolour modelling scheme, where the SU2-branching level meets the initial n(S n)=/G/ condition. We focus on correlative mappings derived from [λ]SA (self-associate) irreps for natural group embeddings and compare these with certain Yamanouchi-Gel'fand chain properties of S 10 Mathematical decompositions of Mλ simple S n-modules with (2≥p≥4)-branchings of λ⊵,λSA (for λ⊢N partitions of n) provide the initial insight into the monocluster spin (NP) physics of [2H]10, [11B]10 (S 10↓D 5), as aspects of (1,12)-(HC)2(11B)10 or (HC)2(2 11B10 carborane cage isotopomers. The questions raised are significant for their impact on CNP nuclear spin weighting of ro-vibrational spectra. The methods used are those of combinatorics-via-group actions, as physical S n-encodings applied to nuclear spin algebras.
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Temme, F. Multicolour models of natural embedding for SU(2≥m≥4)×S 10↓D 5 NMR spin symmetry: Determinacy of nuclear spin weights for (1,12)-car-11B-boranes. Journal of Mathematical Chemistry 24, 133–142 (1998). https://doi.org/10.1023/A:1019118602488
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DOI: https://doi.org/10.1023/A:1019118602488