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An integrable structure related with tridiagonal algebras
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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.
Forward citations
Cited by 3 Pith papers
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Full diagonalization of the Heun-Askey-Wilson operator via algebraic Bethe ansatz and Leonard pairs, including Bethe equations, T-Q relations, and Askey-Wilson polynomial solutions.
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Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra
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The alternating central extension for the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$
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