arXiv subjects
Publications and source records attributed to Cesar Gomez.
We propose a definition of a Poincaré algebra for a two dimensional space--time with one discretized dimension. This algebra has the structure of a Hopf algebra. We use the link between Onsager's uniformization of the Ising model and the dispersion relation of a free particle in this space--time, together with the rapidity representation of the quantum deformation of the Poincaré enveloping algebra.
We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods. An extensive bibliography is also included.
We find new solutions to the Yang--Baxter equation in terms of the intertwiner matrix for semi-cyclic representations of the quantum group $U_q(s\ell(2))$ with $q= e^{2πi/N}$. These intertwiners serve to define the Boltzmann weights of a lattice model, which shares some similarities with the chiral Potts model. An alternative interpretation of these Boltzmann weights is as scattering matrices of solitonic structures whose kinematics is entirely governed by the quantum group. Finally, we consider the limit $N\to\infty$ where we find an infinite--dimensional representation of the braid group, which may give rise to an invariant of knots and links.