Quantum affine algebras and universal functional relations

TL;DR

This paper reviews universal functional relations in quantum integrable systems linked to quantum groups of loop Lie algebras, emphasizing their independence from specific quantum space representations.

Contribution

It introduces the concept of universal functional relations and discusses their structure within quantum groups of loop Lie algebras.

Findings

Universal integrability objects are defined via monodromy and transfer operators.

Universal functional relations are independent of quantum space representations.

The paper provides a concise review of these relations in the context of loop Lie algebra quantum groups.

Abstract

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.