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$^{(1)}_n$, 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.