Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
Year: 1994
Type: article
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.
Authors: ATSUO KUNIBA, TOMOKI NAKANISHI, JUNJI SUZUKI
Institutions: Kyushu University, Harvard University, The University of Tokyo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2009808709