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Using the Fronsdal-Galindo formula for the exponential mapping from thequantum algebra $U_{p,q}(gl(2))$ to the quantum group $GL_{p,q}(2)$, we showhow the $(2j+1)$-dimensional representations of $GL_{p,q}(2)$ can be obtainedby `exponentiating' the well-known $(2j+1)$-dimensional representations of$U_{p,q}(gl(2))$ for $j$ $=$ $1,{3/2},... $; $j$ $=$ 1/2 corresponds to thedefining 2-dimensional $T$-matrix. The earlier results on thefinite-dimensional representations of $GL_q(2)$ and $SL_q(2)$ (or $SU_q(2)$)are obtained when $p$ $=$ $q$. Representations of $U_{\bar{q},q}(2)$ $(q$ $\in$$\C \backslash \R$ and $U_q(2)$ $(q$ $\in$ $\R \backslash \{0\})$ are alsoconsidered. The structure of the Clebsch-Gordan matrix for $U_{p,q}(gl(2))$ isstudied. The same Clebsch-Gordan coefficients are applicable in the reductionof the direct product representations of the quantum group $GL_{p,q}(2)$.Comment: 17 pages, LaTeX (latex twice), no figures. Changes consist of more  general formula (4.13) for T-matrices, explicit Clebsch-Gordan coefficients,  boson realization of group parameters, and typographical correction

Finite-dimensional representations of the quantum group GLp,q(2) using the exponential map from Up,q(gl(2))

Finite-dimensional representations of the quantum group GL_p,q(2) using the exponential map from U_p,q(gl(2))