A Holstein-Primakoff and a Dyson realization for the quantum algebra $U_q[sl(n+1)]$

Details A Holstein-Primakoff and a Dyson realization for the quantum algebra $U_q[sl(n+1)]$ A Holstein-Primakoff and a Dyson realization for the quantum algebra $U_q[sl(n+1)]$

1998-04-03

arxiv.org/abs/math/9804017v1

Mathematics

Quantum Algebra

5 pages, TeX

Scientific paper

10.1088/0305-4470/31/22/014

The known Holstein-Primakoff and Dyson realizations of the Lie algebra
$sl(n+1), n=1,2,...$ in terms of Bose operators (Okubo S 1975 J. Math. Phys. 16
528) are generalized to the class of the quantum algebras $U_q[sl(n+1)]$ for
any $n$. It is shown how the elements of $U_q[sl(n+1)]$ can be expressed via
$n$ pairs of Bose creation and annihilation operators.

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