Abstract
For automorphic spin symmetries over isotopomer networks defining both NMR coherence transfer and cage-cluster ro-vibrational (RV) weighting phenomena, the role of Schur functions (SF) and their SF products (SFP) (restricted to Sn) is re-evaluated, beyond that typical of atomic physics. It is seen now as being equally applicable to molecular physics. Our special focus here is on the SU2 × Sn dual group for its importance in replacing (Jucys) recoupling schemata by generalised Sn democracy invariants, which ensure the retention of simple reducibility (SR) of carrier spaces for superboson mappings, under U × P(Γ) actions over Liouville space, i.e., as in Physica A 198 (1993) 245. SFP mapping onto Sn and simple Young rule SF mappings onto {[λ]}(Sn) sets are developed in the high n-index, weak-branching limit and utilise known similarities in the algorithms for the Young and Littlewood–Richardson rules. Over discrete k rank, from k=n (down), the Σν{/Tk(ν)/x007D;k-set orders are related to the ⊵ ordered bipartite χ 12n [λ] (S2n characters.
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