Representations of Two-Colour BWM Algebras and Solvable Lattice Models

Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour generalization of the Birman-Wenzl-Murakami algebra can be constructed, which in turn are used to derive trigonometric solutions to the Yang-Baxter equation. In spirit, this construction resembles the fusion procedure, in the sense that starting from known solutions of the Yang-Baxter equation new solutions can be obtained.