Application of the eigenfunction method to the icosahedral group

Abstract

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 S12. 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 (m/n)1/2[exp(iφ)]p [2 cos φ]q [2 cos 2φ]r, where m, n, p, q, and r are integers and φ=2π/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 (m/n)1/2.