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Application of the eigenfunction method to the icosahedral group. (English) Zbl 0701.20008

Summary: The group table for the icosahedral group I is constructed by using the isomorphism between the group I and a subgroup of the permutation group \(S_{12}\). The single-valued irreducible representations and Clebsch- Gordan (CG) coefficients of I are calculated by a computer code based on the eigenfunction method. The irreducible matrix elements for all the 60 group elements are given explicitly in the form of \(\sqrt{m/n}[\exp (i\phi)]^ p[2\cos \phi]^ q[2\cos 2\phi]^ r\), where m, n, p, q, and r are integers and \(\phi =2\pi /5\). The Clebsch-Gordan coefficients of I are all real under a new phase convention for time reverse states and tabulated in the form of \(\sqrt{m/n}\).

MSC:

20C35 Applications of group representations to physics and other areas of science
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[2] DOI: 10.1017/S0305004100033156
[3] DOI: 10.1063/1.1731744
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