\((Z_ N\times\;)^{n-1}\) generalization of the chiral Potts model. (English) Zbl 0737.17012
An attempt is made to construct a new solvable lattice model whose Boltzmann weight obeys high genus algebraic relations. It is shown that the \(R\)-matrix which intertwines two \(n\times N^{n-1}\) state cyclic \(L\)-operators related to a generalization of \(U_ q(sl(n))\) can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction. The Yang-Baxter equation for the resulting \(R\)-matrix is verified numerically for \(n=3\), \(N=2\) and conjectured to be valid in the general case. The factorization properties of the \(L\)- operator are studied and its relation to the SOS models is discussed.
Reviewer: P.Kosiński (Łódź)
MSC:
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 82B23 | Exactly solvable models; Bethe ansatz |
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