泛T-矩阵、OSp_q（1/2）和小Q-雅可比多项式的表示
Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials
摘要：
我们得到了包含量子超代数U_q[osp（1/2）]和相应的超群OSp_q（1/2）对偶的泛T矩阵的封闭形式表达式。这个普适T-矩阵的经典q->1极限产生了未变形的OSp（1/2）超群的群元。利用所述泛T矩阵和已知的对偶相关变形超代数U_q[osp（1/2）]的有限维表示，很容易构造出量子超群OSp_q（1/2）的有限维表示.进一步导出了量子超群OSp_q（1/2）的乘积律、递推关系和表示的正交性。证明了这些表示矩阵的元素都表示为Q = -q的小Q-雅可比多项式。给出了泛T-矩阵在泛R-矩阵上的两个互补奇异映射。
英文摘要：
We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp_q(1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed U_q[osp(1/2)] superalgebra. Proceeding further, we derive the product law, the recurrence relations and the orthogonality of the representations of the quantum supergroup OSp_q(1/2). It is shown that the entries of these representation matrices are expressed in terms of the little Q-Jacobi polynomials with Q = -q. Two mutually complementary singular maps of the universal T-matrix on the universal R-matrix are also presented.
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