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The β„€β‚‚ x β„€β‚‚-graded Lie superalgebra π–•π–˜π–”(2m +1|2n) and new parastatistics representations

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Abstract
When the relative commutation relations between a set of m parafermions and n parabosons are of 'relative parafermion type', the underlying algebraic structure is the classical orthosymplectic Lie superalgebra (LSA) osp(2m + 1|2n). The relative commutation relations can also be chosen differently, of 'relative paraboson type'. In this second case, the underlying algebraic structure is no longer an ordinary LSA, but a Z(2) x Z(2)-graded LSA, denoted here by pso(2m+ 1|2n). The identification of this new algebraic structure was performed by Tolstoy, amongst others. In the present paper, we investigate the subalgebra structure of pso(2m + 1|2n). This allows us to study the parastatistics Lock spaces for this new set of m + n para-operators, as they correspond to lowest weight representations of pso(2m + 1|2n). Our main result is the construction of these Lock spaces, with a complete labeling of the basis vectors and an explicit action of the para-operators on these basis vectors.
Keywords
SUPER-ALGEBRAS, FOCK SPACE, PARA-BOSE, STATISTICS, parabosons and parafermions, Z(2) x Z(2)-graded Lie superalgebras, Fock, representations

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Chicago
Stoilova, NI, and Joris Van der Jeugt. 2018. β€œThe β„€β‚‚ x β„€β‚‚-graded Lie Superalgebra π–•π–˜π–”(2m +1|2n) and New Parastatistics Representations.” Journal of Physics A-mathematical and Theoretical 51 (13).
APA
Stoilova, NI, & Van der Jeugt, J. (2018). The β„€β‚‚ x β„€β‚‚-graded Lie superalgebra π–•π–˜π–”(2m +1|2n) and new parastatistics representations. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 51(13).
Vancouver
1.
Stoilova N, Van der Jeugt J. The β„€β‚‚ x β„€β‚‚-graded Lie superalgebra π–•π–˜π–”(2m +1|2n) and new parastatistics representations. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2018;51(13).
MLA
Stoilova, NI, and Joris Van der Jeugt. β€œThe β„€β‚‚ x β„€β‚‚-graded Lie Superalgebra π–•π–˜π–”(2m +1|2n) and New Parastatistics Representations.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 51.13 (2018): n. pag. Print.
@article{8562371,
  abstract     = {When the relative commutation relations between a set of m parafermions and n parabosons are of 'relative parafermion type', the underlying algebraic structure is the classical orthosymplectic Lie superalgebra (LSA) osp(2m + 1|2n). The relative commutation relations can also be chosen differently, of 'relative paraboson type'. In this second case, the underlying algebraic structure is no longer an ordinary LSA, but a Z(2) x Z(2)-graded LSA, denoted here by pso(2m+ 1|2n). The identification of this new algebraic structure was performed by Tolstoy, amongst others. In the present paper, we investigate the subalgebra structure of pso(2m + 1|2n). This allows us to study the parastatistics Lock spaces for this new set of m + n para-operators, as they correspond to lowest weight representations of pso(2m + 1|2n). Our main result is the construction of these Lock spaces, with a complete labeling of the basis vectors and an explicit action of the para-operators on these basis vectors.},
  articleno    = {135201},
  author       = {Stoilova, NI and Van der Jeugt, Joris},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  keyword      = {SUPER-ALGEBRAS,FOCK SPACE,PARA-BOSE,STATISTICS,parabosons and parafermions,Z(2) x Z(2)-graded Lie superalgebras,Fock,representations},
  language     = {eng},
  number       = {13},
  pages        = {17},
  title        = {The \unmatched{2124}\unmatched{2082} x \unmatched{2124}\unmatched{2082}-graded Lie superalgebra π–•π–˜π–”(2m +1|2n) and new parastatistics representations},
  url          = {http://dx.doi.org/10.1088/1751-8121/aaae9a},
  volume       = {51},
  year         = {2018},
}

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