Abstract
The non-generic central elements of the quadratic algebra A1 associated with the quantum group GL(2)q are found in the case where q is a root of unity. A q-boson realization of A1 is constructed. In terms of the q-boson realization the representations of A1 on the q-Fock space are studied in both generic and non-generic cases and the cyclic representation is obtained in the non-generic case.
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