Truncation of the reflection algebra and the Hahn algebra

Nicolas Crampé; Eric Ragoucy; Luc Vinet; Alexei Zhedanov

Truncation of the reflection algebra and the Hahn algebra

Nicolas Crampé ^{1, 2, *} Eric Ragoucy ^{3, *} Luc Vinet ² Alexei Zhedanov ⁴

* Corresponding author

1 IDP - Institut Denis Poisson

2 CRM - Centre de Recherches Mathématiques [Montréal]

3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

4 Renmin University of China

Abstract : 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.

Document type :

Journal articles

Domain :

Mathematics [math] / Mathematical Physics [math-ph]

Mathematics [math] / Quantum Algebra [math.QA]

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https://hal-univ-tours.archives-ouvertes.fr/hal-02305525
Contributor : Sandrine Renard-Riccetti <>
Submitted on : Friday, October 4, 2019 - 11:53:01 AM
Last modification on : Thursday, October 10, 2019 - 1:05:04 AM

1903.05674.pdf

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Truncation of the reflection algebra and the Hahn algebra

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