  The low-energy electronic structure of icosahedral fullerenes is studied
within the field-theory model. In the field model, the pentagonal rings in the
fullerene are simulated by two kinds of gauge fields. The first one,
non-abelian field, follows from so-called K spin rotation invariance for the
spinor field while the second one describes the elastic flow due to pentagonal
apical disclinations. For fullerene molecule, these fluxes are taken into
account by introducing an effective field due to magnetic monopole placed at
the center of a sphere. Additionally, the spherical geometry of the fullerene
is incorporated via the spin connection term. The exact analytical solution of
the problem (both for the eigenfunctions and the energy spectrum) is found.
