The energy spectrum and wave functions of the two dimensional Hubbard
model with infinite repulsion are studied for N x N cluster. The calcu
lations are carried out at pre-assigned total quasimomentum values of
(a) over right arrow. A set of four non-linear algebraic equations is
derived, which describes tl-ie energy levels of the cluster. The analy
ses is reduced to the simplest case a(x) = a(y) = alpha, alpha = (0, p
i).