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

TL;DR

This paper constructs parastatistics Fock spaces as lowest weight representations of a specific infinite-dimensional $Z_2 imes Z_2$-graded Lie superalgebra, using Gelfand-Zetlin patterns.

Contribution

It introduces a new class of Fock spaces for infinite parafermions and parabosons linked to a novel graded Lie superalgebra structure.

Findings

Fock spaces are realized as lowest weight representations.

Basis constructed using row-stable Gelfand-Zetlin patterns.

Provides a framework for understanding parastatistics in algebraic terms.

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.