Generalized chiral Potts models and minimal cyclic representations of $$ {U_q}(\widehat {\mathfrak{g}\mathfrak{l}}(n,C))$$

R-matrices for highest weight representations of at roots of unity

“…As a consequence we obtain new solutions of spectral parameter dependent Yang-Baxter equations. We show also that the intertwiners, considered in [4,5], are particular cases of ones, obtained in [6] by a different approach.…”

“…We can take x 2 = 1, x 1 = x becauseR depends on x 2 x 1 only. Then the equations (6) for g = f 0 , f 1 can be represented in the following form:…”

“…The Yang-Baxter equations on V ξ ⊗ V j ⊗ V j can be proven using the irreducibility of tensor product as in [6]. At the end we write the components ofR(x) : V ξ ⊗ V j ⇒ V j ⊗ V ξ for N = 3, j = 1 2 .…”

Three-dimensional integrable models and associated tangle invariants

“…The key idea of ref. [1] is to describe the Baxter-Bazhanov model as an integrable generalized chiral Potts model [10,11,12] in the IRF presentation by the following prescription. For this aim, one starts from an edge of the bidimensional lattice on which the chiral Potts model is defined.…”

“…One of the most important features [1] of the Baxter-Bazhanov model is that apart from a modification of the boundary conditions it can be obtained as a threedimensional interpretation of the generalized sl(n)-chiral Potts model [10,11,12].…”