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 -11 B-boranes

Abstract

The inherent (in)determinacy implicit in the SU(m≥3)×Sn↓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(Sn)=/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 S10 Mathematical decompositions of Mλ simple Sn-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 (S10↓D5), as aspects of (1,12)-(HC)2(11B)10 or (HC)2(211B10 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 Sn-encodings applied to nuclear spin algebras.