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

• URL: http://arxiv.org/abs/2112.12811v1
• Date: Thu, 23 Dec 2021 19:23:00 GMT
• Title: The $Z_2 \times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty|\infty)$, and parastatistics Fock spaces
• Authors: N.I. Stoilova and J. Van der Jeugt
• Abstract summary: The Fock spaces are lowest weight representations of the $Z times Z$-graded Lie super $pso(infty|infty)$, with a basis consisting of row-stable Gelfand-Zetlin patterns.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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