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Parabosons, parafermions, and explicit representations of infinite-dimensional algebras

(2010) PHYSICS OF ATOMIC NUCLEI. 73(3). p.533-540
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Abstract
The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(infinity) and of the Lie superalgebra osp(1|infinity). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.
Keywords
Lie superalgebras, fermions, Parastatistics, bosons

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Citation

Please use this url to cite or link to this publication:

MLA
Stoilova, Nedialka, and Joris Van der Jeugt. “Parabosons, Parafermions, and Explicit Representations of Infinite-Dimensional Algebras.” PHYSICS OF ATOMIC NUCLEI, vol. 73, no. 3, 2010, pp. 533–40, doi:10.1134/S1063778810030178.
APA
Stoilova, N., & Van der Jeugt, J. (2010). Parabosons, parafermions, and explicit representations of infinite-dimensional algebras. PHYSICS OF ATOMIC NUCLEI, 73(3), 533–540. https://doi.org/10.1134/S1063778810030178
Chicago author-date
Stoilova, Nedialka, and Joris Van der Jeugt. 2010. “Parabosons, Parafermions, and Explicit Representations of Infinite-Dimensional Algebras.” PHYSICS OF ATOMIC NUCLEI 73 (3): 533–40. https://doi.org/10.1134/S1063778810030178.
Chicago author-date (all authors)
Stoilova, Nedialka, and Joris Van der Jeugt. 2010. “Parabosons, Parafermions, and Explicit Representations of Infinite-Dimensional Algebras.” PHYSICS OF ATOMIC NUCLEI 73 (3): 533–540. doi:10.1134/S1063778810030178.
Vancouver
1.
Stoilova N, Van der Jeugt J. Parabosons, parafermions, and explicit representations of infinite-dimensional algebras. PHYSICS OF ATOMIC NUCLEI. 2010;73(3):533–40.
IEEE
[1]
N. Stoilova and J. Van der Jeugt, “Parabosons, parafermions, and explicit representations of infinite-dimensional algebras,” PHYSICS OF ATOMIC NUCLEI, vol. 73, no. 3, pp. 533–540, 2010.
@article{935595,
  abstract     = {{The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(infinity) and of the Lie superalgebra osp(1|infinity). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.}},
  author       = {{Stoilova, Nedialka and Van der Jeugt, Joris}},
  issn         = {{1063-7788}},
  journal      = {{PHYSICS OF ATOMIC NUCLEI}},
  keywords     = {{Lie superalgebras,fermions,Parastatistics,bosons}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{533--540}},
  title        = {{Parabosons, parafermions, and explicit representations of infinite-dimensional algebras}},
  url          = {{http://doi.org/10.1134/S1063778810030178}},
  volume       = {{73}},
  year         = {{2010}},
}

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