The Z2×Z2 -graded Lie superalgebras pso(2n+1|2n) and pso(∞|∞) , and parastatistics Fock spaces

Abstract

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 × Z 2 -graded Lie superalgebra p s o ( ∞ | ∞ ) , with a basis consisting of row-stable Gelfand–Zetlin patterns.