Liu, Fa; Ping, Jialun; Chen, Jinquan Application of the eigenfunction method to the icosahedral group. (English) Zbl 0701.20008 J. Math. Phys. 31, No. 5, 1065-1075 (1990). 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 \(\sqrt{m/n}\). Cited in 2 Documents MSC: 20C35 Applications of group representations to physics and other areas of science Keywords:group table; icosahedral group; irreducible representations; irreducible matrix elements; Clebsch-Gordan coefficients PDFBibTeX XMLCite \textit{F. Liu} et al., J. Math. Phys. 31, No. 5, 1065--1075 (1990; Zbl 0701.20008) Full Text: DOI References: [1] Laporte O., Z. Naturforsch. 3 pp 447– (1948) [2] DOI: 10.1017/S0305004100033156 [3] DOI: 10.1063/1.1731744 [4] DOI: 10.1080/00268977300101981 [5] DOI: 10.1088/0305-4470/13/4/015 · Zbl 0449.20052 [6] DOI: 10.1103/PhysRevLett.53.2477 [7] DOI: 10.1103/RevModPhys.57.211 [8] DOI: 10.1088/0305-4470/16/7/012 · Zbl 0515.22016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.