Abstract
Viruses are organized biological nanosystems which display high levelof spatial organization. In the present work we focus on the group theory methods application to the problems of virus self-assembly and resulting viral structure formation. The approach is based on the successive application of methods of representation theory for continuous and discrete groups and invariant theory for the groups not-generated by reflections. It generalizes the Landau density wave theory of crystallization to the case of compact crystal-like manifold assembly. To compare the predictions of the theory with the available cryoelectronic microscopy data we use the calculated density distribution functions which generate the protein positions on a spherical surface of the cage protecting viral genome. We also discuss therelation between density distribution functions and viral infectivity.