# An integrable structure related with tridiagonal algebras

Abstract : The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on the tridiagonal algebraic structure associated with a deformation parameter $q$. Representations are shown to be generated from a class of quadratic algebras, namely the reflection equations. The spectral problem is briefly discussed. Finally, related massive quantum integrable models are shown to be superintegrable.
Document type :
Journal articles
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https://hal.archives-ouvertes.fr/hal-00019442
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Submitted on : Tuesday, February 21, 2006 - 8:40:59 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM

### Citation

Pascal Baseilhac. An integrable structure related with tridiagonal algebras. Nuclear Physics B, Elsevier, 2005, 705, pp.605-619. ⟨hal-00019442⟩

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