A Quantum group approach to constructing factorizable S matrices

Mauro Melchiades Doria

Michael Lässig, Marcio Jose Martins

Zhan-Ning Hu

In this paper, the factorizable S matrices with toroidal rapidity values are constructed explicitly and the symmetry operators of which tensor product commutes with S are found. These operators have a structure which is similar to the ordinary Hopf algebra. As a limit of the elliptic case sl q (2) quantum algebra with q N = 1 can be obtained from the symmetry operators.

M. Ruiz-Altaba

These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December 1992. They constitute a brief and elementary introduction to quantum symmetries from a physical point of view, along the lines of the forthcoming book by C. Gómez, G. Sierra, and myself: 1) Introduction. 2) Factorizable S‐matrices. 3) Bethe’s diagonalization of spin chain hamiltonians. 4) Integrable vertex models: the six‐vertex model. 5) The Yang‐Baxter algebra. 6) Physical spectrum of the Heisenberg spin chain. 7) Yang‐Baxter algebras and braid groups. 8) Yang‐Baxter algebras and quantum groups. 9) Affine quantum groups. 10) Hopf algebras. 11) The quantum group Uq(G). 12) Comments. 13) References.

Людвиг Дмитриевич Фаддеев

David V. Chudnovsky, Gregory V. Chudnovsky