A LISP System for Chemical Groups: Wigner — Eckart Coefficients for Arbitrary Permutation Groups
Computer applications of group theory have almost invariably used numerical representations of the fundamental quantities of the group. For example, the combination laws in the crystallographic groups have been described as matrix multiplications on tables of coordinates . These decimal values are approximate specifications of in principle exactly equivalent points. The finite mathematics realized in computers does not permit the numerical operations to represent faithfully the group theoretic operations.
Symbolic manipulation systems make possible an exact representation of the combination laws of a group, and the exact calculation of the characters, irreducible representations, and coupling coefficients which symmetry-adapt primitive bases. We illustrate how the small MuMATH (Registered trade mark of the Soft Warehouse) system can generate properties of the permutation groups useful in the analysis of NMR spectra of flexible or rearranging systems. The work rests on the properties of semi-direct products, as described by Altmann .
KeywordsIrreducible Representation Permutation Group Semidirect Product Double Coset Pair Exchange
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