  In this article, I analyze the symmetries and degeneracies of electron
eigenstates in a commensurate collinear antiferromagnet. In a magnetic field
transverse to the staggered magnetization, a hidden anti-unitary symmetry
protects double degeneracy of the Bloch eigenstates at a special set of
momenta. In addition to this `Kramers degeneracy' subset, the manifold of
momenta, labeling the doubly degenerate Bloch states in the Brillouin zone, may
also contain an `accidental degeneracy' subset, that is not protected by
symmetry and that may change its shape under perturbation. These degeneracies
give rise to a substantial momentum dependence of the transverse g-factor in
the Zeeman coupling, turning the latter into a spin-orbit interaction.
  I discuss a number of materials, where Zeeman spin-orbit coupling is likely
to be present, and outline the simplest properties and experimental
consequences of this interaction, that may be relevant to systems from chromium
to borocarbides, cuprates, hexaborides, iron pnictides, as well as organic and
heavy fermion conductors.
