The Quantum Superalgebra ospq(1|2) and a q-Generalization of the Bannai-Ito Polynomials
Abstract
The Racah problem for the quantum superalgebra ospq(1|2) is considered. The intermediate Casimir operators are shown to realize a q-deformation of the Bannai-Ito algebra. The Racah coefficients of ospq(1|2) are calculated explicitly in terms of basic orthogonal polynomials that q-generalize the Bannai-Ito polynomials. The relation between these q-deformed Bannai-Ito polynomials and the q-Racah/Askey-Wilson polynomials is discussed.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- June 2016
- DOI:
- 10.1007/s00220-016-2647-2
- arXiv:
- arXiv:1501.05602
- Bibcode:
- 2016CMaPh.344..465G
- Keywords:
-
- Orthogonal Polynomial;
- Recurrence Relation;
- Casimir Operator;
- Superintegrable System;
- Wilson Polynomial;
- Mathematics - Quantum Algebra;
- Mathematical Physics;
- Mathematics - Classical Analysis and ODEs
- E-Print:
- 15 pages