Dilute Birman--Wenzl--Murakami Algebra and $D^{(2)}_{n+1}$ models

TL;DR

This paper introduces a dilute generalization of the Birman--Wenzl--Murakami algebra, which can be Baxterised to produce solutions to the Yang--Baxter algebra, leading to new solvable lattice models related to $D^{(2)}_{n+1}$.

Contribution

It develops a dilute algebra framework that extends existing algebraic structures and connects to solvable lattice models of type $D^{(2)}_{n+1}$, broadening the algebraic tools for integrable systems.

Findings

Constructed a dilute Birman--Wenzl--Murakami algebra.

Baxterisation yields solutions to the Yang--Baxter equation.

Identified $D^{(2)}_{n+1}$ models as dilute versions of $B^{(1)}_{n}$ models.

Abstract

A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra. The $D^{(2)}_{n+1}$ vertex models are examples of corresponding solvable lattice models and can be regarded as the dilute version of the $B^{(1)}_{n}$ vertex models.