On the symmetries of integrable systems with boundaries

TL;DR

This paper explores the symmetries of integrable systems with boundaries by using affine Hecke algebra realizations to find solutions to the reflection equation and analyze the symmetry properties of open spin chains.

Contribution

It introduces a method to recover known non-diagonal solutions of the reflection equation for quantum affine algebras and demonstrates their role in revealing system symmetries.

Findings

Recovered non-diagonal solutions of the reflection equation for $U_q( ilde{gl}_n)$

Established symmetry properties of open spin chains with specific boundary conditions

Analyzed the symmetry of the local Hamiltonian in boundary integrable systems

Abstract

We employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the $U_{q}(\hat{gl_n})$ case. With the help of linear intertwining relations involving the aforementioned solutions of the reflection equation, the symmetry of the open spin chain with a particular choice of the left boundary is exhibited. The symmetry of the corresponding local Hamiltonian is also explored.