Solvable RSOS models based on the dilute BWM algebra

In this paper we present representations of the recently introduced dilute Birman-Wenzl-Murakami algebra. These representations, labelled by the level-l B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ 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_n+1⁽²⁾, A_2n⁽²⁾ and B_n⁽¹⁾R-matrices of Bazhanov and Jimbo. For the D_n+1⁽²⁾ and B_n⁽¹⁾ 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.