Abstract. Using the Fronsdal-Galindo formula for the exponential mapping from the quantum algebra U_p,q(gl(2)) to the quantum group GL_p,q(2), we show how the (2j+1)-dimensional representations of GL_p,q(2) can be obtained by 'exponentiating' the well known (2j+1)-dimensional representations of U_p,q(gl(2)) for j=1, 3/2, ...; j= 1/2 corresponds to the defining two-dimensional T-matrix. The earlier results on the finite-dimensional representations of GL_q(2) and SL_q(2) (or SU_q(2)) are obtained when p=q. Representations of U_q,q(2)(q in C mod R) and U_q(2)(q in R mod (0)) are also considered. The structure of the Clebsch-Gordan matrix for U_p,q(gl(2)) is studied. The same Clebsch-Gordan coefficients are applicable in the reduction of the direct product representations of the quantum group GL_p,q(2).

Print publication: Issue 10 (21 May 1995)