  We investigate several spin-related phenomena in a confined two-dimensional
electron gas (2DEG) using the Hartree-Fock approximation for the mutual Coulomb
interaction of the electrons. The exchange term of the interaction causes a
large splitting of the spin levels whenever the chemical potential lies within
a Landau band (LB). This splitting can be reinterpreted as an enhancement of an
effective g-factor, g*. The increase of g* when a LB is half filled can be
accompanied by a spontaneous formation of a static spin-inversion state (SIS)
whose details depend on the system sision state (SIS) whose details depend on
the system size. The coupling of the states of higher LB's into the lowest band
by the Coulomb interaction of the 2DEG is essential for the SIS to occur. The
far-infrared absorption of the system, relatively insensitive to the spin
splitting, develops clear signs of the SIS.
