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