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.

arXiv comment15 pages

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Cited by in corpus (10)

• The Z_2 x Z_2-graded Lie superalgebra pso(2m+1|2n) and new parastatistics representations
• The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces
• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• Partition functions and thermodynamic properties of paraboson and parafermion systems
• Representations of the Lie superalgebra $B(\infty ,\infty )$ and parastatistics Fock spaces
• Extension of the osp(m|n)~ so(m-n) Correspondence to the Infinite-Dimensional Chiral Spinors and Self Dual Tensors
• Gel'fand-Zetlin basis for a class of representations of the Lie superalgebra gl(\infty|\infty)
• Generalized Quantum Statistics and Lie (Super)Algebras
• A Klein operator for paraparticles
• On characters and superdimensions of some infinite-dimensional irreducible representations of $\mathfrak{osp}(m|n)$