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.
Categories: hep-th