  The polarization of direct photons produced in an ultrarelativistic heavy-ion
collision reflects the momentum anisotropy of the quark-gluon plasma created in
the collision. This paper presents a general framework, based on the photon
spectral functions in the plasma, for analyzing the angular distribution and
thus the polarization of dileptons in terms of the plasma momentum
anisotropies. The rates of dilepton production depend, in general, on four
independent spectral functions, corresponding to two transverse polarizations,
one longitudinal polarization, and -- in plasmas in which the momentum
anisotropy is not invariant under parity in the local rest frame of the matter
-- a new spectral function, $\rho_n$, related to the anisotropy direction in
the collision. The momentum anisotropy appears in the difference of the two
transverse spectral functions, as well as in $\rho_n$. As an illustration, we
delineate the spectral functions for dilepton pairs produced in the lowest
order Drell-Yan process of quark-antiquark annihilation to a virtual photon.
