Truncation of the reflection algebra and the Hahn algebra

Nicolas Crampé (1, 2) , Eric Ragoucy (3) , Luc Vinet (2) , Alexei Zhedanov (4)

1 IDP - Institut Denis Poisson
2 CRM - Centre de Recherches Mathématiques [Montréal]
3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique
4 Department of Mathematics [Renmin]

In the context of connections between algebras coming from quantum integrable systems and algebras associated to the orthogonal polynomials of the Askey scheme, we prove that the truncated reflection algebra attached to the Yangian of sl2 is isomorphic to the Hahn algebra. As a by-product, we provide a general setup based on Euler polynomials to study truncations of reflection algebras.

Domains: Mathematics [math]; Mathematical Physics [math-ph]; Mathematics [math]; Quantum Algebra [math.QA]

Nicolas Crampé, Eric Ragoucy, Luc Vinet, Alexei Zhedanov. Truncation of the reflection algebra and the Hahn algebra. Journal of Physics A: Mathematical and Theoretical, 2019, 52 (35), pp.35LT01. ⟨10.1088/1751-8121/ab32f8⟩. ⟨hal-02305525⟩