Abstract
The author considers the irreducible representations of the Onsager algebra, and shows that for a finite system, possessing such an algebra leads to an Ising-like structure in the spectra of associated Hamiltonians and transfer matrices. The chiral Potts model is considered as an example. For transfer in the diagonal direction, it is known to be superintegrable. For transfer in the principal direction, a new superintegrable solution manifold is found.
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