# Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid

@article{Loday2008ParastatisticsAY,
title={Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid},
author={Jean-Louis Loday and Todor Popov},
journal={International Journal of Geometric Methods in Modern Physics},
year={2008},
volume={05},
pages={1295-1314}
}
• Published 5 October 2008
• Mathematics
• International Journal of Geometric Methods in Modern Physics
The parastatistics algebra is a superalgebra with (even) parafermi and (odd) parabose creation and annihilation operators. The states in the parastatistics Fock-like space are shown to be in one-to-one correspondence with the Super Semistandard Young Tableaux (SSYT) subject to further constraints. The deformation of the parastatistics algebra gives rise to a monoidal structure on the SSYT which is a super-counterpart of the plactic monoid.
We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded two-step nilpotent
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## References

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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
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The analog of the plactic monoid for the super semistandard Young tableaux over a signed alphabet is constructed by developing a generalization of the Knuth's relations by getting generalizations of Greene's invariants and Young–Pieri rule.
Abstract:The paper contains essentially two new results. Physically, a deformation of the parastatistics in a sense of quantum groups is carried out. Mathematically, an alternative to the Chevalley
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It is known that the defining relations of the orthosymplectic Lie superalgebra $${\mathfrak{osp}(1|2n)}$$ are equivalent to the defining (triple) relations of n pairs of paraboson operators
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