Hidden Symmetry of the Racah and Clebsch-Gordan Problems for the Quantum Algebra sl_q(2)
Ya. I. Granovskii, A. S. Zhedanov
TL;DR
This paper reveals a hidden symmetry algebra, Askey-Wilson algebra, underlying the Racah and generalized Clebsch-Gordan problems for quantum algebra sl_q(2), enabling a new method to compute related coefficients using Askey-Wilson polynomials.
Contribution
It introduces the Askey-Wilson algebra as a hidden symmetry for these problems and proposes a straightforward calculation method for the coefficients involved.
Findings
Askey-Wilson algebra underpins Racah and Clebsch-Gordan problems for sl_q(2)
A new method to compute coefficients using Askey-Wilson polynomials
Simplification of calculations in quantum algebra representations
Abstract
The Askey-Wilson algebra with three generators is shown to serve as a hidden symmetry algebra underlying the Racah and (new) generalized Clebsch-Gordan problems for the quantum algebra . On the base of this hidden symmetry a simple method to calculate corresponding coefficients in terms of the Askey-Wilson polynomials is proposed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Quantum chaos and dynamical systems