N(exp n(n-1)/2)-state R-matrix related with U(sub q)(sl(n)) algebra at q(exp 2N) = 1

Rinat Kashaev, Vladimir V. Mangazeev

Tetsuo Deguchi

We review the main result of cond-mat/0503564.The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl 2 loop algebra symmetry if the q parameter is given by a root of unity, q 2N 0 = 1, for an integer N .We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regular Bethe ansatz eigenvector in the sectors is a highest weight vector and derive the highest weight d± k , which leads to evaluation parameters a j .If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state.

A. Lima-Santos, W. Galléas

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

We present N3-state R-matrix related with Uq(sl(3)) algebra at q2N=1. Its matrix elements are interpreted as Boltzmann weights of an elementary box of some 2d lattice statistical model and given in terms of [Formula: see text] weights of the "minimal" sl(3) chiral Potts model.

Yongqing Chen, Bolin Yu

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.