Hecke algebraic approach to the reflection equation for spin chains
A Doikou, P P Martin
TL;DR
This paper introduces a novel algebraic approach using Hecke algebras and Coxeter Artin systems to generate solutions to the reflection equation for spin chains, along with Bethe ansatz states.
Contribution
It develops a new method connecting Coxeter Artin systems with the reflection equation, providing explicit solutions and Bethe ansatz states based on abstract representation theory.
Findings
New solutions to the reflection equation derived from Coxeter Artin systems
Construction of Bethe ansatz states using algebraic parameterization
Establishment of a structural link between algebraic systems and integrable models
Abstract
We use the structural similarity of certain Coxeter Artin Systems to the Yang--Baxter and Reflection Equations to convert representations of these systems into new solutions of the Reflection Equation. We construct certain Bethe ansatz states for these solutions, using a parameterisation suggested by abstract representation theory.
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