  In its most general formulation a quantum kinematical system is described by
a Heisenberg group; the "configuration space" in this case corresponds to a
maximal isotropic subgroup. We study irreducible models for Heisenberg groups
based on compact maximal isotropic subgroups. It is shown that if the
Heisenberg group is 2-regular, but the subgroup is not, the "vacuum sector" of
the irreducible representation exhibits a fermionic structure. This will be the
case, for instance, in a quantum mechanical model based on the 2-adic numbers
with a suitably chosen isotropic subgroup. The formulation in terms of
Heisenberg groups allows a uniform treatment of p-adic quantum systems for all
primes p, and includes the possibility of treating adelic systems.
