Cyclic L operators connected with U-q(sl(n)) algebra and related integrable models

E. K. Sklyanin

Nir Sochen

Shi-shyr Roan

We identify the precise relationship between the five-parameter τ (2) -family in the N -state chiral Potts model and XXZ chains with U q ( sl 2 )-cyclic representation. By studying the Yang–Baxter relation of the six-vertex model, we discover a one-parameter family of L -operators in terms of the quantum group U q ( sl 2 ). When N is odd, the N -state τ (2) -model can be regarded as the XXZ chain of cyclic representations with . The symmetry algebra of the τ (2) -model is described by the quantum affine algebra via the canonical representation. In general, for an arbitrary N , we show that the XXZ chain with a U q ( sl 2 )-cyclic representation for q 2 N = 1 is equivalent to two copies of the same N -state τ (2) -model.

Rinat Kashaev, Vladimir V. Mangazeev, Yu. G. Stroganov

Using an eight-state cyclic L-operator related to the Uq( sl (3)) algebra at q2 = -1 we have found an interwining eight-state R-matrix in the "trigonometric" limit. Corresponding commuting family of transfer matrices depends on three independent spectral parameters.

Marcio Jose Martins

A. Kundu