A description of the quantum superalgebra $U_q[sl(n+1\mathrm{\mid }m)]$ via creation and annihilation generators

A description of the quantum superalgebra $U_q[sl(n+1\mathrm{\mid }m)]$ and in particular of the special linear superalgebra $sl(n+1\mathrm{\mid }m)$ via creation and annihilation generators (CAGs) is given. It provides an alternative to the canonical description of $U_q[sl(n+1\mathrm{\mid }m)]$ in terms of Chevalley generators. A conjecture that the Fock representations of the CAGs provide microscopic realizations of exclusion statistics is formulated.