Hidden symmetry of Hahn problem for $sl_q(2)
A.N.Lavrenov
TL;DR
This paper reveals a hidden symmetry algebra within the Hahn problem for $sl_q(2)$, connecting it to the Askey-Wilson algebra, and derives related Clebsch-Gordan coefficients using q-Hahn polynomials.
Contribution
It identifies a special case of the Askey-Wilson algebra as the hidden symmetry of the Hahn problem for $sl_q(2)$ and computes the associated Clebsch-Gordan coefficients.
Findings
Hidden symmetry algebra is a special case of Askey-Wilson algebra.
Clebsch-Gordan coefficients are expressed in terms of q-Hahn polynomials.
Provides new algebraic insight into the Hahn problem for quantum algebra $sl_q(2)$.
Abstract
A special case of Askey-Wilson algebra with three generators is shown to serve as a hidden symmetry algebra underlying the Hahn problem for the quantum algebra . On the base of this hidden symmetry the corresponding Clebsch-Gordan coefficients in terms of the q-Hahn polynomials is found.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Mathematical functions and polynomials · Advanced Combinatorial Mathematics