LATTICE ALGEBRAS AND THE HIDDEN SYMMETRY OF THE 2D ISING-MODEL IN A MAGNETIC-FIELD

Lattice algebras are defined and used to study the symmetries of 2D lattice models. New and interesting examples of such algebras are provided by the affine Hecke algebra, owing to the possibility of constructing braid generators out of its generators. I propose an Ansatz for the braid generators and derive some solutions. A particular finite-dimensional quotient is shown to be a natural generalization of the Temperley-Lieb-Jones algebra. It is used to give a unified picture of known and unknown symmetries of the spin-1/2 xxz model with boundary terms. The Ising model in an external magnetic field is also a representation of this quotient.