  Using semi-analytic modeling techniques, we calculate the luminosity function
of galaxy populations residing in cold dark matter halos of different mass. We
pay particular attention to the influence of the reionization of the Universe
on the number of faint galaxies and to the effects of dynamical friction and
tidal limitation of satellites on the number of bright galaxies. We find
substantial differences in the shapes of the galaxy luminosity functions in
halos of different mass which reflect generic features of the cold dark matter
model of galaxy formation and thus offer the opportunity to test it. We then
consider how the individual halo luminosity functions combine together to
produce the global luminosity function. Surprisingly, the global function ends
up having a shallower faint end slope than those of the constituent halo
luminosity functions. We compare our model predictions with the limited
datasets compiled by Trentham & Hodgkin. We find good agreement with the
luminosity functions measured in the Virgo and Coma clusters but significant
disagreement with the luminosity functions measured in the Local Group and Ursa
Minor cluster. We speculate on possible inadequacies in our modeling and in the
existing observational samples. The luminosity functions of galaxies in groups
and clusters identified in the 2dF and SDSS galaxy redshift surveys offer the
prospect of testing galaxy formation models in detail.
