Algebraic expressions for irreducible bases of icosahedral group

The recently discovered point-group symmetrized boson representation (SBR) is constructed for the icosahedral group I-h. With the aid of the SBR, succinct algebraic expressions for the irreducible bases and irreducible matrices have been found. Irreducible bases for non-regular representations can be found easily from those of the regular representation without projections. Explicit expressions of the irreducible bases are given for the molecule B12H12 for several important cases. It is shown that, far from being ''chaotic'' in structure, the 120 irreducible matrices of I-h have a high degree of symmetry in that the 14 400 entries can be reproduced from a few dozen entries according to three rules. (C) 1997 American Institute of Physics.