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

Abstract

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 [?p/2, ⋯ -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.