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

TL;DR

This paper constructs explicit infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n), relates them to parastatistics Fock spaces, and derives character formulas using supersymmetric Schur functions.

Contribution

It introduces a new class of lowest weight representations of osp(2m+1|2n), explicitly constructs their basis and transformation rules, and connects them to parastatistics Fock spaces with character formulas.

Findings

Explicit basis and transformation rules for the representations.

Construction of the parastatistics Fock space of order p.

Derivation of character formulas using supersymmetric Schur functions.

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.