The theoretical background of the work was published by Peter Goldreich and his at the time postdoc Nick Kylafis[1] in a series of two papers in The Astrophysical Journal.
The GK effect predicts that, under special conditions, the spectral lines emitted by interstellar molecules should be linearly polarized and the linear polarization vector should reveal the magnetic field direction in the molecular cloud.
If the magnetic sublevels of the J=1 level are equally populated, as it is usually the case, then the line is unpolarized.
Goldreich & Kylafis (1981)[2] showed that, if the radiation field (their own plus external) in which the molecules are embedded is anisotropic, then the magnetic sublevels are unequally populated.
Since isotropic radiation fields are practically non existent in Nature (e.g. only at the center of an isolated perfectly spherical molecular cloud), the effect should be easily detectable.