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

Author:

KUNIBA ATSUO1,NAKANISHI TOMOKI2,SUZUKI JUNJI3

Affiliation:

1. Department of Mathematics, Kyushu University, Fukuoka 812, Japan

2. Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA

3. Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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