Abstract
The method of q-deformed boson realization is extended to the case that q is a root of unity. By using the method, many irreducible and indecomposable representations of each subalgebra in a subalgebra chain of the quantum universal enveloping algebra (quantum algebra) (Cl)q are obtained on the q-deformed Fock space and its quotient space. As an example, the representations of (C3)q are constructed in explicit forms. Besides, by embedding (A1)q = (C1)q, into the subalgebra chain, a new realisation of (A1)q and its representations are obtained.
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