  It is shown theoretically that Bose condensation of spin-degenerated
exciton-polaritons results in spontaneous buildup of the linear polarization in
emission spectra of semiconductor microcavities. The linear polarization degree
is a good order parameter for the polariton Bose condensation. If
spin-degeneracy is lifted, an elliptically polarized light is emitted by the
polariton condensate. The main axis of the ellipse rotates in time due to
self-induced Larmor precession of the polariton condensate pseudospin. The
polarization decay time is governed by the dephasing induced by the
polariton-polariton interaction and strongly depends on the statistics of the
condensed state.
