  It is known that the defining triple relations of m pairs of parafermion
operators and n pairs of paraboson operators with relative parafermion
relations can be considered as defining relations for the Lie superalgebra
osp(2m+1|2n) in terms of 2(m+n) generators. With the common Hermiticity
conditions, this means that the parastatistics Fock space of order p
corresponds to an infinite-dimensional unitary irreducible representation V(p)
of osp(2m+1|2n), with lowest weight (-p/2,...,- p/|p/2,...,p/2). These
representations (also in the simplest case m=n=1) had never been constructed
due to computational difficulties, despite their importance. In the present
paper we solve partially the problem in the general case using group
theoretical techniques, in which the u(m|n) subalgebra of osp(2m+1|2n) plays a
crucial role: a set of Gelfand-Zetlin patterns of u(m|n) can be used to label
the basis vectors of V(p). An explicit and elegant construction of these
representations V(p) for m=n=1, and the actions or matrix elements of the
osp(3|2) generators are given.
