The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces

Abstract

The parastatistics Fock spaces of order $p$ corresponding to an infinite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces are lowest weight representations of the $Z_2\times Z_2$-graded Lie superalgebra $pso(\infty |\infty )$, with a basis consisting of row-stable Gelfand-Zetlin patterns.

arXiv admin note: text overlap with arXiv:1904.00061

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• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
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• $\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra
• On the detectability of paraparticles beyond bosons and fermions
• Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework