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The coherent state method has proved to be useful in quantum physics andmathematics. This method, more precisely, the vector coherent state method, hasbeen used by some authors to construct representations of superalgebras butalmost, to our knowledge, it has not yet been extended to quantumsuperalgebras, except $U_q[osp(1|2)]$, one of the smallest quantumsuperalgebras. In this article the method is applied to a bigger quantumsuperalgebra, namely $U_q[gl(2|1)]$, in constructing $q$--boson-fermionrealizations and finite-dimensional representations which, when irreducible,are classified into typical and nontypical representations. This constructionleads to a more general class of $q$--boson-fermion realizations andfinite-dimensional representations of $U_q[gl(2|1)]$ and, thus, at $q=1$, of$gl(2|1)$. Both $gl(2|1)$ and $U_q[gl(2|1)]$ have found different physicsapplications, therefore, it is meaningful to construct their representations.

Representations of quantum superalgebra Uq[gl(2|1)] in a coherent state basis and generalization