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Onsager’s algebra and superintegrability. (English) Zbl 0718.17026

Irreducible representations of finite-dimensional Onsager algebras are considered. It is examined that the transfer matrices in the principal direction may be diagonalised using Onsager’s algebra. The chiral Potts model is considered as an example. For transfer in the principal direction, a new superintegrable solution manifold is found.

MSC:

17B99 Lie algebras and Lie superalgebras
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
17B81 Applications of Lie (super)algebras to physics, etc.
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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