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Representations of the Lie superalgebra B(infinity, infinity) and parastatistics Fock spaces

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Abstract
The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion relations, is known to be the Lie superalgebra osp(2m + 1 vertical bar 2n). The Fock spaces of such systems are then certain lowest weight representations of osp(2m + 1 vertical bar 2n). In the current paper, we investigate what happens when the number of parafermions and parabosons becomes infinite. In order to analyze the algebraic structure, and the Fock spaces, we first need to develop a new matrix form for the Lie superalgebra B(n, n) = osp(2n + 1 vertical bar 2n), and construct a new Gelfand-Zetlin basis of the Fock spaces in the finite rank case. The new structures are appropriate for the situation n -> infinity. The algebra generated by the infinite number of creation and annihilation operators is B(infinity, infinity), a well defined infinite rank version of the orthosymplectic Lie superalgebra. The Fock spaces are lowest weight representations of B(infinity, infinity), with a basis consisting of particular row-stable Gelfand-Zetlin patterns.
Keywords
PARA-BOSE, Lie superalgebra, parastatistics, Fock space

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Chicago
Stoilova, N., I, and Joris Van der Jeugt. 2019. “Representations of the Lie Superalgebra B(infinity, Infinity) and Parastatistics Fock Spaces.” Journal of Physics A-mathematical and Theoretical 52 (13).
APA
Stoilova, N., I., & Van der Jeugt, J. (2019). Representations of the Lie superalgebra B(infinity, infinity) and parastatistics Fock spaces. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 52(13).
Vancouver
1.
Stoilova, N. I, Van der Jeugt J. Representations of the Lie superalgebra B(infinity, infinity) and parastatistics Fock spaces. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. Bristol: Iop Publishing Ltd; 2019;52(13).
MLA
Stoilova, N., I, and Joris Van der Jeugt. “Representations of the Lie Superalgebra B(infinity, Infinity) and Parastatistics Fock Spaces.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 52.13 (2019): n. pag. Print.
@article{8608502,
  abstract     = {The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion relations, is known to be the Lie superalgebra osp(2m + 1 vertical bar 2n). The Fock spaces of such systems are then certain lowest weight representations of osp(2m + 1 vertical bar 2n). In the current paper, we investigate what happens when the number of parafermions and parabosons becomes infinite. In order to analyze the algebraic structure, and the Fock spaces, we first need to develop a new matrix form for the Lie superalgebra B(n, n) = osp(2n + 1 vertical bar 2n), and construct a new Gelfand-Zetlin basis of the Fock spaces in the finite rank case. The new structures are appropriate for the situation n -{\textrangle} infinity. The algebra generated by the infinite number of creation and annihilation operators is B(infinity, infinity), a well defined infinite rank version of the orthosymplectic Lie superalgebra. The Fock spaces are lowest weight representations of B(infinity, infinity), with a basis consisting of particular row-stable Gelfand-Zetlin patterns.},
  articleno    = {135201},
  author       = {Stoilova, N., I and Van der Jeugt, Joris},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  language     = {eng},
  number       = {13},
  pages        = {28},
  publisher    = {Iop Publishing Ltd},
  title        = {Representations of the Lie superalgebra B(infinity, infinity) and parastatistics Fock spaces},
  url          = {http://dx.doi.org/10.1088/1751-8121/ab09bc},
  volume       = {52},
  year         = {2019},
}

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