A new braid-like algebra for Baxterisation

TL;DR

This paper introduces a novel algebraic approach for Baxterisation of R-matrices with two spectral parameters, enabling the derivation of R-matrices for multi-species exclusion processes with varying rates.

Contribution

A new algebraic framework close to the braid group is proposed for Baxterisation, extending the class of R-matrices accessible for integrable models.

Findings

Recovered R-matrix for multi-species TASEP with different hopping rates

Developed a new algebraic structure for Baxterisation

Enhanced understanding of spectral parameter dependence in R-matrices

Abstract

We introduce a new Baxterisation for R-matrices that depend separately on two spectral parameters. The Baxterisation is based on a new algebra, close to but different from the braid group. This allows us to recover the R-matrix of the multi-species generalization of the totally asymmetric simple exclusion process with different hopping rates.