Influence of deformation on the energy and optical absorption spectra of fullerene C$_{20}$ within the Hubbard model

Anticommutator Green's functions and energy spectra of fullerene C$_{20}$ with the $I_h$, $D_{5d}$, and $D_{3d}$ symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C$_{20}$ with the $I_h$, $D_{5d}$, and $D_{3d}$ symmetry groups have been determined. It is also shown how the energy levels of fullerene C$_{20}$ with the $I_h$ symmetry group are split with the symmetry reduction.