Yamanouchi-chain Sn-invariant hierarchies for SR carrier space of {Tk(v)}(SU2×Sn) dual tensors in NMR: some maximal Sn-inner products, via Sn-restricted-space Schur Fn. product mappings Original Research

The permutation field aspects of {Tkmax−i(k1,..kn)}(SU2×Sn) sets are considered within Latin-square constructions, i.e. based on (bi-part) {λ̂} Schur functions(fns.) (SFs) and their product mappings onto {{λ̂}} sets (restricted to Sn) taken in the high n-index, weak-branching (WB) limit. Certain new maximal inner products [λ]×[λ′] are proven, via Schur fn. product (SFP) differences and SFP-on-Sn maps in the above limit. An interesting role in defining tensorial subspaces is established for the bi-part S2n characters. This defines ∀ 1≤i≤n the cardinality of each Σv/{Tkmax−i(v)}/ k-rank-subspace, within that of the full rank space, 2nn. The spin algebras discussed here determine both the complete nuclear permutation(CNP) physics of cage isotopomers (i.e., via the ro-vibrational weightings) and the nature of coherence transfer phenomena over NMR networks. Indeed, their derived {[λ̃]}(Sn) sets play a central role in defining subduction via Yamanouchi-Gelʹfand chains and their monomial reduction coefficients. Hence, each system invariant is realised essentially as a labelling hierarchy for a distinct pathway over the full Sn⊃..⊃S2 subduction chain. The motivation for this modelling of invariants came from the observed auxiliary v=(11)..sʹ role in J-coupling (or coherence transfer), and from the well-known analytic limitation under high degeneracy to the democratisation of pure quantum systems.