Universal Tmatrix, representations of OSp{sub q}(1/2) and little QJacobi polynomials
Abstract
We obtain a closed form expression of the universal Tmatrix 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 Tmatrix 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 abovementioned universal Tmatrix 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 QJacobi polynomials with Q=q. Two mutually complementary singular maps of the universal Tmatrix on the universal Rmatrix are also presented.
 Authors:
 Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Daisen Campus, Sakai, Osaka 5900035 (Japan)
 (India)
 Publication Date:
 OSTI Identifier:
 20861568
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2399360; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DUALITY; GROUP THEORY; JACOBIAN FUNCTION; POLYNOMIALS; QUANTUM MECHANICS; R MATRIX; RECURSION RELATIONS; S MATRIX; SUPERSYMMETRY
Citation Formats
Aizawa, N., Chakrabarti, R., Mohammed, S. S. Naina, Segar, J., Department of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600 025, and Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600 004. Universal Tmatrix, representations of OSp{sub q}(1/2) and little QJacobi polynomials. United States: N. p., 2006.
Web. doi:10.1063/1.2399360.
Aizawa, N., Chakrabarti, R., Mohammed, S. S. Naina, Segar, J., Department of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600 025, & Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600 004. Universal Tmatrix, representations of OSp{sub q}(1/2) and little QJacobi polynomials. United States. doi:10.1063/1.2399360.
Aizawa, N., Chakrabarti, R., Mohammed, S. S. Naina, Segar, J., Department of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600 025, and Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600 004. Fri .
"Universal Tmatrix, representations of OSp{sub q}(1/2) and little QJacobi polynomials". United States.
doi:10.1063/1.2399360.
@article{osti_20861568,
title = {Universal Tmatrix, representations of OSp{sub q}(1/2) and little QJacobi polynomials},
author = {Aizawa, N. and Chakrabarti, R. and Mohammed, S. S. Naina and Segar, J. and Department of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600 025 and Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai 600 004},
abstractNote = {We obtain a closed form expression of the universal Tmatrix 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 Tmatrix 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 abovementioned universal Tmatrix 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 QJacobi polynomials with Q=q. Two mutually complementary singular maps of the universal Tmatrix on the universal Rmatrix are also presented.},
doi = {10.1063/1.2399360},
journal = {Journal of Mathematical Physics},
number = 12,
volume = 47,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}

The infinite dimensional highest weight representations of U{sub q}osp(1{vert_bar}2) for the deformation parameter q being a root of unity are investigated. As in the cases of qdeformed nongraded Lie algebras, we find that every irreducible representation is isomorphic to the tensor product of a highest weight representation of sl{sub 2}(R) and a finite dimensional one of U{sub q}osp(1{vert_bar}2). The structure is investigated in detail. {copyright} {ital 1997 American Institute of Physics.}

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