On spin irreps of (1 Ii 3) 12-fold uniform NMR spin systems as invariant-based dual tensorial sets: Roles in spin physics for weight sets and their -partitional frequency catalogues

A direct systematic approach is given to the derivation of outer M-labelled {|IM(.)>} dual (spin) irrep sets for identical n [Formula: see text] 12-fold higher Ii nuclear spin ensembles, stressing (i) the essential role of multipartite partitions in spin physics, (ii) the value of algorithmic tableaux-based decompositions in the subsequent [Formula: see text]n combinatorical modelling, and (iii) how the dual group invariants (based on time-reversal invariance) govern the auxiliary labels of specialized dual tensors. Such (uniform inner rank) dual group basis sets (spin representations) underlie both NMR and isotopomer CNP spectral weightings. Specific applications are discussed here to illustrate the value of number partitional-based designs for statistical frequencies and recent algorithmic "sst" ([Formula: see text]n)-encoding techniques in quantized spin physics of uniform higher spin sets. In addition, a democratic recoupled form of purely SU(2) × [Formula: see text]2n projective modelling for the dual group invariants (SI) is given via an augmented democratic form of Weyl time-reversal invariance (TRV), over some regular solid geometry. From simple lattice-point geometric constraints, a maximal (2n)-index limit is established for global NMR ensemble spin symmetry. PACS Nos.: 02.10De, 02.20-a, 05.36Ch, 11.30Er, 33.25+k, 33.20Vq