  We introduce and describe in second quantization a family of particle species
with \(p=2,3,\dots\) exclusion and \(\theta=2\pi/p\) exchange statistics. We
call these anyons Fock parafermions, because they are the particles naturally
associated to the parafermionic zero-energy modes, potentially realizable in
mesoscopic arrays of fractional topological insulators. Their
second-quantization description entails the concept of Fock algebra, i.e., a
Fock space endowed with a statistical multiplication that captures and
logically correlates these anyons' exclusion and exchange statistics. As a
consequence normal-ordering continues to be a well-defined operation. Because
of its relevance to topological quantum information processing, we also derive
families of self-dual representations of the braid group for any $p$, with the
Gaussian representation being a special case. The self-dual representations can
be realized in terms of local quadratic combinations of either parafermions or
Fock parafermions, an important requisite for physical implementation of
quantum logic gates.
