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# Deformed Dolan-Grady relations in quantum integrable models

Abstract : A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators $\\{\\textsf{A}, \\textsf{A}^*\\}\\in{\\cal A}$ subject to $q-$deformed Dolan-Grady relations. Using the inverse scattering method, a new family of quantum integrable models is proposed. In the simplest case, the Hamiltonian is linear in the fundamental generators of ${\\cal A}$. For general values of $q$, the corresponding spectral problem is quasi-exactly solvable. Several examples of two-dimensional massive/massless (boundary) integrable models are reconsidered in light of this approach, for which the fundamental generators of ${\\cal A}$ are constructed explicitly and exact results are obtained. In particular, we exhibit a dynamical Askey-Wilson symmetry algebra in the (boundary) sine-Gordon model and show that asymptotic (boundary) states can be expressed in terms of $q-$orthogonal polynomials.
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https://hal.archives-ouvertes.fr/hal-00019441
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Submitted on : Tuesday, February 21, 2006 - 8:39:14 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM

### Citation

Pascal Baseilhac. Deformed Dolan-Grady relations in quantum integrable models. Nuclear Physics B, Elsevier, 2005, 709, pp.491-521. ⟨hal-00019441⟩

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