Integrable boundary conditions for multi-species ASEP

TL;DR

This paper introduces explicit solutions for integrable boundary conditions in multi-species ASEP models, revealing a new algebraic structure that extends the boundary Hecke algebra.

Contribution

It provides novel explicit boundary solutions for multi-species ASEP and uncovers a new algebraic framework beyond the boundary Hecke algebra.

Findings

Explicit boundary solutions for multi-species ASEP

Introduction of a new algebraic structure extending boundary Hecke algebra

Demonstration of the solutions' integrability properties

Abstract

The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper.