  We address theoretically the optical parametric oscillator based on
semiconductor cavity exciton-polaritons under a pulsed excitation. A
"hyperspin" formalism is developed which allows, in the case of large number of
polaritons, to reduce quantum dynamics of the parametric oscillator
wavefunction to the Liouville equation for the classical probability
distribution. Implications for the statistics of polariton ensembles are
analyzed.
