A class of infinite-dimensional representations of the Lie superalgebra osp(2m + 1|2n) and the parastatistics Fock space

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+ 1 vertical bar 2n) is introduced. These representations are particular lowest weight representations V(p), with a lowest weight of the form [ -p/2 ,..., -p/2 vertical bar p/2 ,..., p/2], p being a positive integer. Explicit expressions for the transformation of the basis under the action of algebra generators are found. Since the relations of algebra generators correspond to the defining relations of m pairs of parafermion operators and n pairs of paraboson operators with relative parafermion relations, the parastatistics Fock space of order p is also explicitly constructed. Furthermore, the representations V(p) are shown to have interesting characters in terms of supersymmetric Schur functions, and a simple character formula is also obtained