  G_2 Yang--Mills theory is an interesting laboratory to investigate
non-perturbative effects. On one hand, no conventional quark confinement via a
linearly rising potential is present. On the other hand, its thermodynamic
properties are similar to ordinary SU(N) Yang--Mills theory. Finally, it has
been conjectured that gluons are removed from the physical spectrum in the same
way as in SU(N) Yang--Mills theory. The last claim will be explored by
determining the Landau-gauge ghost and gluon propagators, as well as the
Faddeev--Popov operator eigenspectrum, in G_2 lattice gauge theory in two and
three dimensions. The results are found to agree qualitatively with the SU(2)
and SU(3) case. Therefore, the conjecture that Yang--Mills theories with
different gauge groups are qualitatively similar on the level of their Landau
gauge Green's functions is supported.
