Truncation of the reflection algebra and the Hahn algebra

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 sl(2) is isomorphic to the Hahn algebra. As a by-product, we provide a general set-up based on Euler polynomials to study truncations of reflection algebras.

References in corpus (8)

• Deformed Dolan-Grady relations in quantum integrable models
• A new (in)finite dimensional algebra for quantum integrable models
• A deformed analogue of Onsager's symmetry in the XXZ open spin chain
• Representations of reflection algebras
• A higher rank Racah algebra and the ${\mathbb{Z}}_2^n$ Laplace-Dunkl operator
• Coideal algebras from twisted Manin triples
• Twisted Yangians and folded W-algebras
• FRT presentation of the Onsager algebras

Cited by in corpus (7)

• The Askey-Wilson algebra and its avatars
• Entanglement of Free Fermions on Johnson Graphs
• Racah problems for the oscillator algebra, the Lie algebra ${\mathfrak{sl}}_n$, and multivariate Krawtchouk polynomials
• New realizations of algebras of the Askey-Wilson type in terms of Lie and quantum algebras
• Bethe ansatz diagonalization of the Heun-Racah operator
• A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial $\mathcal{P}\mathcal{T}$-symmetry and Higgs algebra
• A Howe correspondence for the algebra of the $\mathfrak{osp}(1|2)$ Clebsch-Gordan coefficients