Universal T-matrix, representations of OSp{sub q}(1/2) and little Q-Jacobi polynomials

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2399360· OSTI ID:20861568

Aizawa, N; Chakrabarti, R; Mohammed, S S. Naina; Segar, J ^[1]

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1. 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, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
DUALITY
GROUP THEORY
JACOBIAN FUNCTION
POLYNOMIALS
QUANTUM MECHANICS
R MATRIX
RECURSION RELATIONS
S MATRIX
SUPERSYMMETRY