Quantum groups and functional relations for lower rank

Abstract

A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum group ${\mathrm{U}}_q(\mathcal{L}({\mathfrak{sl}}_2))$ is given. The full proof of the functional relations in the form independent of the representation of the quantum group on the quantum space is presented. The case of the general gradation and general twisting is treated. The specialization of the universal functional relations to the case when the quantum space is the state space of a discrete spin chain is described. This is a degression of the corresponding consideration for the case of the quantum group ${\mathrm{U}}_q(\mathcal{L}({\mathfrak{sl}}_3))$ with an extensions to the higher spin case.

arXiv commentSubstantially extended talks given by the authors at the Wilhelm und Else Heraeus-Seminar "Integrable Lattice Models and Quantum Field Theories", June 28 - July 2, 2014, Bad Honnef, Germany