Quantum group symmetry of integrable models on the half-line

TL;DR

This paper explores the quantum group symmetries in integrable models on the half-line, deriving non-local conserved charges and solutions to the reflection equation, revealing new algebraic structures.

Contribution

It introduces new symmetry algebras as coideals of quantum groups for sine-Gordon and affine Toda models on the half-line, and connects intertwiners to solutions of the reflection equation.

Findings

Derived non-local conserved charges for models on the half-line

Identified new symmetry algebras as coideals of quantum groups

Established a method to find solutions to the reflection equation

Abstract

This contribution to the Proceedings of the Workshop on Integrable Theories, Solitons and Duality in Sao Paulo in July 2002 summarizes results from the papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved charges in the sine-Gordon model and affine Toda field theories on the half-line. They generate new kinds of symmetry algebras that are coideals of the usual quantum groups. We show how intertwiners of tensor product representations of these algebras lead to solutions of the reflection equation. We describe how this method for finding solutions to the reflection equation parallels the previously known method of using intertwiners of quantum groups to find solutions to the Yang-Baxter equation.