Universal T-matrix, representations of OSp{sub q}(1/2) and little Q-Jacobi polynomials
- Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Daisen Campus, Sakai, Osaka 590-0035 (Japan)
We obtain a closed form expression of the universal T-matrix encapsulating the duality between the quantum superalgebra U{sub q}[osp(1/2)] and the corresponding supergroup OSp{sub q}(1/2). The classical q{yields}1 limit of this universal T-matrix yields the group element of the undeformed OSp{sub q}(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp{sub q}(1/2) are readily constructed employing the above-mentioned universal T-matrix and the known finite dimensional representations of the dually related deformed U{sub 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{sub 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.
- OSTI ID:
- 20861568
- Journal Information:
- Journal of Mathematical Physics, Vol. 47, Issue 12; Other Information: DOI: 10.1063/1.2399360; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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