Explicit computation of orthonormal symmetrized harmonics with applicationto the identity representation of the icosahedral group

A novel method to explicitly compute orthonormal symmetrized harmonics is p resented and the method is applied to the identity representation of the ic osahedral group. Spherical viruses have icosahedral symmetry and the motiva ting application is the parametric representation of spherical viruses for use in inverse problems based on x-ray scattering data and cryoelectron mic roscopy images. The symmetrized harmonics are computed in the form of linea r combinations of spherical harmonics of one order and therefore have simpl e rotational properties which is valuable in the electron microscopy applic ation. The method is based on equating the expansions of a symmetrized delt a function in spherical and in symmetrized harmonics from which bilinear eq uations for the weights in the linear combinations can be derived. The expl icit character of the calculation is reflected in the fact that both explic it expressions and an efficient recursive algorithm are derived for computi ng the weights in the linear combinations.