Solvable RSOS models based on the dilute BWM algebra

TL;DR

This paper introduces new solvable RSOS models based on the dilute BWM algebra, providing explicit representations and solutions to the Yang-Baxter equation, including novel models for certain affine Lie algebra series.

Contribution

It presents new representations of the dilute BWM algebra and constructs solvable RSOS models, including novel models for D^{(2)}_{n+1} and B^{(1)}_n series, with elliptic extensions.

Findings

Constructed Baxterized solutions to the Yang-Baxter equation.

Introduced new RSOS models for D^{(2)}_{n+1} and B^{(1)}_n series.

Provided elliptic extensions for all three series.

Abstract

In this paper we present representations of the recently introduced dilute Birman-Wenzl-Murakami algebra. These representations, labelled by the level-$l$ B$^{(1)}_n$, C$^{(1)}_n$ and D$^{(1)}_n$ affine Lie algebras, are Baxterized to yield solutions to the Yang-Baxter equation. The thus obtained critical solvable models are RSOS counterparts of the, respectively, D$^{(2)}_{n+1}$, $A^{(2)}_{2n}$ and B$^{(1)}_n$ $R$-matrices of Bazhanov and Jimbo. For the D$^{(2)}_{n+1}$ and B$^{(1)}_n$ algebras the RSOS models are new. An elliptic extension which solves the Yang-Baxter equation is given for all three series of dilute RSOS models.