  We report on first principles Self-Interaction Corrected LSD (SIC-LSD)
calculations of electronic structure of LaMnO$_{3}$ in the cubic phase. We
found a strong tendency to localisation of the Mn $e_{g}$ electron and to
orbital ordering. We found the ground state to be orbitally ordered with a
staggered order of $x^{2}-z^{2}$ and $y^{2}-z^{2}$ orbits in one plane and this
order is repeated along the third direction. The difference in energy with a
solution consisting of the ordering of $3x^{2}-r^{2}$ and $3y^{2}-r^{2}$ is,
however, very small. The latter ordering is similar to the one observed both
experimentally and theoretically in the real distorted system. The system is in
the insulating A-type antiferromagnetic ordered state in both cases. The
presence of orbital ordering means breaking of the cubic symmetry and without
recourse to distortion. The latter may rather be the result of the orbital
ordering but the symmetry of this ordering is determined by coupling to the
lattice. The strong tendency to localisation of the $e_{g}$ electron in
LaMnO$_{3}$ accounts for the survival of local distortions above the structural
phase transition temperature.
