Algebraic construction of higher-rank dilute A models Original Research Article

Starting from representations of the Birman-Wenzl-Murakami algebra underlying the critical Bn(1), Cn(1) and Dn(1) RSOS models of Jimbo, Miwa and Okado, we derive four series of solvable, critical RSOS models associated with the twisted affine Lie algebra An(2). Two of these are the critical limit of the A2n−1(2) and A2n(2) models obtained previously by Kuniba. The other two series, again one of the A2n−1(2) and one of the A2n(2) type, are new, and the latter generalizes the dilute A models to arbitrary rank n. For the two new series we present an elliptic extension which satisfies the Yang-Baxter equation, and show that for certain values of the parameters the higher-rank dilute A models break the ℤ2 symmetry of the underlying adjacency graphG, whereGis the level-l Cn(1) weight lattice.