The Z2×Z2 -graded Lie superalgebras pso(2n+1|2n) and pso(∞|∞) , 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 ℤ2 × ℤ2-graded Lie superalgebra pso(∞|∞), with a basis consisting of row-stable Gelfand-Zetlin patterns.

ℤ2 × ℤ2-graded Lie algebras and supseralgebras and related physical models

“…Z 2 ×Z 2 -graded Lie superalgebras , their mathematical properties and symmetries generated by these superalgebras in physical systems attract renewed attention in recent years [4] - [17].…”