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

## Abstract

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.

- Authors:

- Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Daisen Campus, Sakai, Osaka 590-0035 (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 T-matrix, representations of OSp{sub q}(1/2) and little Q-Jacobi 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 T-matrix, representations of OSp{sub q}(1/2) and little Q-Jacobi 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 T-matrix, representations of OSp{sub q}(1/2) and little Q-Jacobi polynomials". United States.
doi:10.1063/1.2399360.
```

```
@article{osti_20861568,
```

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

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}

}