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We obtain a closed form expression of the universal T-matrix encapsulatingthe duality of the quantum superalgebra U_q[osp(1/2)] and the correspondingsupergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrixyields the group element of the undeformed OSp(1/2) supergroup. The finitedimensional representations of the quantum supergroup OSp_q(1/2) are readilyconstructed employing the said universal T-matrix and the known finitedimensional representations of the dually related deformed U_q[osp(1/2)]superalgebra. Proceeding further, we derive the product law, the recurrencerelations and the orthogonality of the representations of the quantumsupergroup OSp_q(1/2). It is shown that the entries of these representationmatrices are expressed in terms of the little Q-Jacobi polynomials with Q = -q.Two mutually complementary singular maps of the universal T-matrix on theuniversal R-matrix are also presented.Comment: 21pages, no figure; final form for publicatio

Universal T-matrix, representations of OSpq(1∕2) and little Q-Jacobi polynomials