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Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials

N. Aizawa·R. Chakrabarti·S. S. Naina Mohammed·J. Segar
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Abstract

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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N. Aizawa, R. Chakrabarti, S. S. Naina Mohammed, J. Segar. 2006-12-28. Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials. https://doi.org/10.1063/1.2399360

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