Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics

TL;DR

This paper constructs Fock space representations for the Lie superalgebra sl(n+1|m) and its quantum version U_q[sl(n+1|m)], exploring their algebraic structures and associated quantum statistics.

Contribution

It provides explicit Fock space representations of superalgebras and their quantum analogues using creation and annihilation operators, advancing understanding of their algebraic and statistical properties.

Findings

Explicit Fock representations for superalgebras and their quantum analogues.

Description of the superalgebras via creation and annihilation operators.

Discussion of the properties of the underlying quantum statistics.

Abstract

Fock space representations of the Lie superalgebra $sl(n+1|m)$ and of its quantum analogue $U_q[sl(n+1|m)]$ are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The properties of the underlying statistics are shortly discussed.