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.

11 pages; LaTeX file with amssymb; ; v2: typos corrected, one reference added, to appear in Nucl. Phys. B