Theta function parameterization and fusion for 3-D integrable Boltzmann weights

@inproceedings{Gehlen2003ThetaFP,
title={Theta function parameterization and fusion for 3-D integrable Boltzmann weights},
author={Gunther Gehlen and S. Pakuliak and Sergei Sergeev},
year={2003}
}

We report progress in constructing Boltzmann weights for integrable 3dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can be conveniently parameterized in terms of N -th roots of theta-functions on the Jacobian of a compact algebraic curve. Fay’s identity guarantees the Fermat relations and the classical equations of motion for the parameters determining the Boltzmann weights. Our parameterization allows to write a simple… CONTINUE READING