A Dyson realization and a Holstein-Primakoff realization for the quantum superalgebra $U_q[gl(n/m)]$

摘要

The Holstein-Primakoff and the Dyson realizations of the Lie superalgebra$gl(n/m)$ are generalized to the class of the quantum superalgebras$U_q[gl(n/m)]$ for any $n$ and $m$. It is shown how the elements of$U_q[gl(n/m)]$ can be expressed via $n-1$ pairs of Bose creation andannihilation operators and $m$ pairs of Fermi creation and annihilationoperators.