Natural embedding of group in NMR spin algebras

NMR aspects of finite group natural-embeddings in higher n-fold spin algebras over Hilbert space are considered in the context of icosahedral cage clusters associated with specific ¹¹B borohydride, -deuteride anions for which n = 12. The focus of the discussion is on the abstract and physical models derived from permutation modules in the form of λ ├ n partitions over , where . Hence, the related Kostka expansion coefficients from the pure abstract spin space of mapping and other -combinatorial aspects, including the nature of inner tensor products arising in the high-n limit, are especially pertinent. Further insight into spin cluster NMR problems is provided by studies of -induced algebras derived from the [λ_SA] self-associated irreps. Motivation for the work comes from its potential physical applications for higher-n bi-cluster NMR problems, e.g., in spin dynamics. The representational properties derived are essential in understanding the structure of Liouville space for both SU(2) and higher spin SU(m) clusters. The Hilbert space aspects presented here impact strongly on the somewhat neglected question of the nature of subduction, i.e., involving a finite group naturally embedded in a higher group, within an implicit dual Racah symmetry chain. The essential mappings presented here include both the λ module-onto-{[λ′]} set and the aspects, where the Kostka integers of the former arise naturally in the realization of λ module mappings over .