PARAFERMIONS, PARABOSONS AND REPRESENTATIONS OF 𝔰𝔬(∞) AND 𝔬𝔰𝔭(1|∞)

DOI10.1142/S0129167X09005467zbMath1181.81128arXiv0801.3909MaRDI QIDQ5324406

Neli I. Stoilova, Joris Van der Jeugt

Publication date: 3 August 2009

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3909

zbMATH Keywords

representationsparafermioninfinite-dimensional Lie (super)algebrasparaboson Fock spaces

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (3)

The Parastatistics Fock Space and Explicit Infinite-Dimensional Representations of the Lie Superalgebra $${\mathfrak {osp}}(2m+1|2n)$$ osp ( 2 m + 1 | 2 n ) ⋮ Representations of the Lie superalgebra $ \newcommand{\B}{\mathfrak{B}} {\B(\infty,\infty)}$ and parastatistics Fock spaces ⋮ Gradings, braidings, representations, paraparticles: some open problems

Cites Work

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• Highest weight irreducible unitary representations of Lie algebras of infinite matrices. I. The algebra gl(∞)
• A braided look at Green ansatz for parabosons
• A Lie superalgebraic interpretation of the para-Bose statistics
• On the Representations of the Semisimple Lie Groups. II
• The parafermion Fock space and explicit \mathfrak{so}(2n+1) representations
• A Generalized Method of Field Quantization
• A generalization of field quantization and statistics
• Lie superalgebras

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