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|2n) is introduced. These representations are particular lowest weight representations V (p), with a lowest weight of the form [−p2 , . . . ,− p 2 | 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. Running title: Lie superalgebra osp(2m+ 1|2n) and parastatistics PACS numbers: 03.65.-w, 03.65.Fd, 02.20.-a, 11.10.-z