Solvable RSOS models based on the dilute BWM algebra

Abstract

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.

25 pages, uuencoded compressed PostScript file, Amsterdam preprint ITFA-94-21

References in corpus (6)

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• Solvable lattice models labelled by Dynkin diagrams
• On the construction of integrable dilute ADE models
• Multi-Colour Braid-Monoid Algebras
• Dilute Birman--Wenzl--Murakami Algebra and $D_{n+1}^{(2)}$ models
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• Enumeration of idempotents in diagram semigroups and algebras
• Critical RSOS Models in External Fields
• New R-matrices from Representations of Braid-Monoid Algebras based on Superalgebras
• Critical points in coupled Potts models and critical phases in coupled loop models
• Dilute Birman--Wenzl--Murakami Algebra and $D_{n+1}^{(2)}$ models
• An integrable modification of the critical Chalker-Coddington network model
• The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
• Exactly soluble isotropic spin-1/2 ladder models
• Yang-Baxter algebras based on the two-colour BWM algebra
• Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models
• Representations of Two-Colour BWM Algebras and Solvable Lattice Models
• Idempotents and homology of diagram algebras