Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami Algebra

TL;DR

This paper presents explicit expressions for three series of R matrices linked to a dilute generalization of the Birman--Wenzl--Murakami algebra, including known and new series with potential applications in quantum integrable systems.

Contribution

The paper provides explicit formulas for three R matrix series related to a dilute Birman--Wenzl--Murakami algebra, introducing two potentially new series.

Findings

One series matches quantum R matrices of D^{(2)}_{n+1} Toda systems

Two series are newly identified and appear to be novel

Explicit expressions facilitate further research in quantum algebra and integrable models

Abstract

Explicit expressions for three series of $R$ matrices which are related to a ``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of those, one series is equivalent to the quantum $R$ matrices of the $D^{(2)}_{n+1}$ generalised Toda systems whereas the remaining two series appear to be new.