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Monodromy matrices of the $tau_2$ model are known to satisfy a Yang--Baxter equation with a six-vertex $R$-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this $R$-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an $L({mathfrak{sl}}_2)$ quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.
We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models, by combining Entings finite lattice method (FLM) with exact transfer matrix enumerations. The models encompass all integra
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These models are desc
We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are di
We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to emph{stable patterns} and emph{signed-patterns}, we give general re
We construct lattice parafermions for the $Z(N)$ chiral Potts model in terms of quasi-local currents of the underlying quantum group. We show that the conservation of the quantum group currents leads to twisted discrete-holomorphicity (DH) conditions