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

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

1998-04-13

arxiv.org/abs/math/9804062v1

Mathematics

Quantum Algebra

7 pages, TeX

Scientific paper

10.1142/S0217732399000341

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.

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