  We present a theoretical model of a driven-dissipative spin-orbit coupled
Bose-Einstein condensate of indirect excitons in semiconductor quantum wells
(QW's). Our steady-state solution of the problem shares analogies with the
Hanle effect in an optical orientation experiment. The role of the spin pump in
our case is played by boson stimulated scattering into the linearly-polarized
ground state and the depolarization occurs as a result of long-range exchange
interaction between electrons and holes. Our theory agrees with the recent
experiment [A. A. High et al., Phys. Rev. Lett. 110, 246403 (2013)], where
spontaneous emergence of spatial coherence and polarization texture have been
observed. As a complementary test, we discuss a configuration where an external
magnetic field is applied in the structure plane.
