Quantum affine algebras and universal functional relations

23rd International Conference on Integrable Systems and Quantum Symmetries

Nirov, Kh S.^1,2 ; Razumov, A.V.^3

Institute for Nuclear Research, Russian Academy of Sciences, 60th October Ave 7a, Moscow

117312, Russia^1

Fachbereich C - Physik, Bergische Universitat Wuppertal, Wuppertal

42097, Germany^2

Institute for High Energy Physics, NRC Kurchatov Institute, Protvino, Moscow region

142281, Russia^3

关键词: Auxiliary space;    Functional relation;    Integrability;    Integrable systems;    Loop Lie algebra;    Monodromy;    Quantum groups;    R matrices;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012037/pdf
DOI  :  10.1088/1742-6596/670/1/012037

来源: IOP

【 摘 要 】

By the universal integrability objects we mean certain monodromy-type and transfer- type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is actually determined by the structure of the universal R-matrix. We call functional relations between such universal integrability objects, and so, being independent of the representation in the quantum space, the universal functional relations. We present a short review of the universal functional relations for the quantum integrable systems associated with the quantum groups of loop Lie algebras.