Contrasting routes to the Kostka coefficients of λ [boxvr] n (ln)-permutational module expansions for 6⩽n⩽8: Applications to NMR spin clusters under SU(m⩽n)×Ln spin symmetries

F.P. Temme

Physica A: Statistical Mechanics and its Applications, 1994, vol. 210, issue 3, 435-452

Abstract: Aspects of the higher-n λ(ln) permutational modules associated with Young subgroups of various highly-branched high-n fold algebras, which are pertinent to identical spin NMR clusters, are presented for λ [boxvr] n (or λ [boxvR] n), aRota p-tuple or number partition; the method of optimal choice for deriving the Λ[λ′] Kostka coefficients, found in {[λ′]} sets derived from λ permutational module expansions, rests on the ordering of the λ-(shape) to the self-associated diagram(s) in the dominance hierarchy. Hence, physical insight into these cage-cluster NMR systems is developed both from these properties and from the inter-related induced symmetries of GL(n, ) and ln groups. From these associated combinatorial, mapping or scalar invariant aspects of SU(m⩽n)× ln symmetry, one may define the [A]n(ln) systems of [AX]n NMR problems in a general semi-topological limit. This corresponds to a high-nln limit in which the individual spin cluster exhibits a lack of any (intracluster) ‘magnetic equivalence’ properties.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:210:y:1994:i:3:p:435-452

DOI: 10.1016/0378-4371(94)90091-4

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