A systematic procedure is developed for constructing fermion systems in
discrete space-time which have a given outer symmetry. The construction is
illustrated by simple examples. For the symmetric group, we derive constraints
for the number of particles. In the physically interesting case of many
particles and even more space-time points, this result shows that the
permutation symmetry of discrete space-time is always spontaneously broken by
the fermionic projector.Comment: 43 pages, LaTeX, few typos corrected (published version
