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 DolanGrady 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.
 Publication:

Nuclear Physics B
 Pub Date:
 January 2005
 DOI:
 10.1016/j.nuclphysb.2004.11.014
 arXiv:
 arXiv:mathph/0408025
 Bibcode:
 2005NuPhB.705..605B
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematics  Mathematical Physics;
 Mathematics  Quantum Algebra;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 11 pages