FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY

1993/09/30 by A. Kuniba, ATSUO KUNIBA, T. Nakanishi +3 · 5 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Ansatz #Bethe ansatz #Functional equation #Lattice (music) #Limit (mathematics) #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Representation (politics) #Simple (philosophy) #hep-th

paper · pdf · doi:10.1142/s0217751x94002119

published as Int.J.Mod.Phys.A9:5215-5266,1994 · 58 pages, 16 eps figures, harvamc.tex epsf.tex (minor corrections, no change in the result)

arxiv created 1994/05/28 · openalex publication_date 1994/12/10 · arxiv updated 2011/05/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite-dimensional quantum group modules is clarified. We find a curious phenomenon where the solutions of those functional relations also solve the so-called thermodynamic Bethe ansatz equations in the high temperature limit for sl(r+1) models. Based on this observation, we propose possible functional relations for models associated with all the simple Lie algebras. We show that these functional relations certainly fulfill strong constraints coming from the fusion procedure analysis. The application to the calculations of physical quantities will be presented in the subsequent paper.

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