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

Abstract

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 and annihilation operators and $m$ pairs of Fermi creation and annihilation operators.

7 pages, TeX

References in corpus (2)

• A Holstein-Primakoff and a Dyson realization for the quantum algebra $U_q[sl(n+1)]$
• A description of the quantum superalgebra $U_q[sl(n+1|m)]$ via creation and annihilation generators

Cited by in corpus (2)

• Jacobson generators of the quantum superalgebra $U_q[sl(n+1|m)]$ and Fock representations
• The $q$-boson-fermion realizations of quantum suprealgebra $U_q(gl(2/1))$