Fusion of Dilute $A_L$ Lattice Models

Abstract

The fusion procedure is implemented for the dilute $A_L$ lattice models and a fusion hierarchy of functional equations with an $su(3)$ structure is derived for the fused transfer matrices. We also present the Bethe ansatz equations for the dilute $A_L$ lattice models and discuss their connection with the fusion hierarchy. The solution of the fusion hierarchy for the eigenvalue spectra of the dilute $A_L$ lattice models will be presented in a subsequent paper.

45 pages; Latex file; epsf.tex needed for graphs

References in corpus (7)

• Order Parameters of the Dilute A Models
• Lattice Ising model in a field: E${}_8$ scattering theory
• Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras
• Exceptional structure of the dilute A${}_3$ model: E${}_8$ and E${}_7$ Rogers--Ramanujan identities
• Fusion of \ade Lattice Models
• Dilute Birman--Wenzl--Murakami Algebra and $D_{n+1}^{(2)}$ models
• Lattice realizations of unitary minimal modular invariant partition functions

Cited by in corpus (15)

• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Scaling Limit of the Ising Model in a Field
• Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
• The principal indecomposable modules of the dilute Temperley-Lieb algebra
• Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model
• An Ising model in a magnetic field with a boundary
• Quantum Jacobi-Trudi Formula and $E_8$ Structure in the Ising Model in a Field
• The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
• Critical behaviour of the dilute O(n), Izergin-Korepin and dilute $A_L$ face models: Bulk properties
• Excited State TBA for the ${\varphi }_{2,1}$ perturbed $M_{3,5}$ model
• Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• The dilute A_L models and the integrable perturbations of unitary minimal CFTs
• The dilute A_L models and the Phi_{1,2} perturbation of unitary minimal CFTs
• Representations of Two-Colour BWM Algebras and Solvable Lattice Models