A class of infinite-dimensional representations of the Lie superalgebra $\mathfrak{o}\mathfrak{s}\mathfrak{p}(2m+1|2n)$ and the parastatistics Fock space

DOI10.1088/1751-8113/48/15/155202zbMath1328.17009arXiv1502.07656OpenAlexW2201745872MaRDI QIDQ5248733

Neli I. Stoilova, Joris Van der Jeugt

Publication date: 8 May 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.07656

zbMATH Keywords

lowest weight representationsclass of infinite-dimensional representations of orthosymplectic Lie superalgebraorthogonal basis of weight vectorsparafermion operators

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Simple, semisimple, reductive (super)algebras (17B20)

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The Parastatistics Fock Space and Explicit Infinite-Dimensional Representations of the Lie Superalgebra $${\mathfrak {osp}}(2m+1|2n)$$ osp ( 2 m + 1 | 2 n ) ⋮ The Z2×Z2 -graded Lie superalgebras pso(2n+1|2n) and pso(∞|∞) , and parastatistics Fock spaces ⋮ Representations of the Lie superalgebra $ \newcommand{\B}{\mathfrak{B}} {\B(\infty,\infty)}$ and parastatistics Fock spaces ⋮ Orthosymplectic Z2×Z2Z2×Z2 -graded Lie superalgebras and parastatistics ⋮ A Klein operator for paraparticles ⋮ Partition functions and thermodynamic properties of paraboson and parafermion systems ⋮ Extension of the $\mathfrak{o}\mathfrak{s}\mathfrak{p}(m|n)\sim \mathfrak{s}\mathfrak{o}(m-n)$ correspondence to the infinite-dimensional chiral spinors and self dual tensors ⋮ The “odd” Gelfand-Zetlin basis for representations of general linear Lie superalgebras ⋮ The $ \newcommand{\Z}{{{\mathbb Z}}} \Z_2\times\Z_2$ -graded Lie superalgebra $ \newcommand{\pso}{\mathfrak{pso}} \pso(2m+1\vert 2n)$ and new parastatistics representations

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