(Quantum) twisted Yangians: symmetry, Baxterisation and centralizers

TL;DR

This paper explores the structure and symmetries of (quantum) twisted Yangians, revealing their role in integrable systems with special boundary conditions, and introduces a new algebraic framework for Baxterisation in the trigonometric case.

Contribution

It analyzes subalgebras of (quantum) twisted Yangians, their symmetry properties, and introduces a novel algebra for Baxterisation in SNP integrable systems.

Findings

Subalgebras provide exact symmetries of the transfer matrix.

Spectrum can be obtained from special boundary types.

New algebraic framework for Baxterisation in the trigonometric case.

Abstract

Based on the (quantum) twisted Yangians, integrable systems with special boundary conditions, called soliton non-preserving (SNP), may be constructed. In the present article we focus on the study of subalgebras of the (quantum) twisted Yangians, and we show that such a subalgebra provides an exact symmetry of the rational transfer matrix. We discuss how the spectrum of a generic transfer matrix may be obtained by focusing only on two types of special boundaries. It is also shown that the subalgebras, emerging from the asymptotics of tensor product representations of the (quantum) twisted Yangian, turn out to be dual to the (quantum) Brauer algebra. To deal with general boundaries in the trigonometric case we propose a new algebra, which also provides the appropriate framework for the Baxterisation procedure in the SNP case.