Abstract
A parametrized cyclic representation of the q-deformed Heisenberg–Weyl algebras is constructed. The cyclic representations of any quantum algebras are studied in terms of their q-boson realizations. A general method to construct the q-boson realizations of quantum algebras from their Verma representations is proposed. Two explicit examples sl(2)q and sl(3)q are studied in detail. Some cyclic representations of quantum algebras sl(n)q and UqCn are presented by using their q-boson realizations.
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