Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]
| Autor: | J. Segar, R. Chakrabarti, Naruhiko Aizawa, S. S. Naina Mohammed |
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| Rok vydání: | 2007 |
| Předmět: |
Statistics and Probability
Pure mathematics General Physics and Astronomy FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Noncommutative geometry Classical limit Superalgebra Modeling and Simulation Mathematics::Quantum Algebra Mathematics - Quantum Algebra FOS: Mathematics Mathematics::Mathematical Physics Quantum Algebra (math.QA) Covariant transformation Hypergeometric function Representation (mathematics) Mathematics::Representation Theory Supergroup Quantum Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.math/0701242 |
| Popis: | Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be expressed in terms of the $Q$-Hahn polynomials. We next investigate representations of the quantum supergroup OSp_q(1/2) which are not well-defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup OSp_q(1/2). Comment: 16 pages, no figures |
| Databáze: | OpenAIRE |
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