edited by Michio Jimbo (Kyoto Univ.)

Table of Contents (131k)
Preface (52k)
Chapter 1: Pioneering Works (6,576k)

This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.

• Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction (C N Yang)
• S matrix for the One Dimensional N-Body Problem with Repulsive or Attractive δ-Function Interaction (C N Yang)
• Partition Function of the Eight-Vertex Lattice Model (R J Baxter)
• Solutions of the Classical Yang-Baxter Equation and Simple Lie Algebras (A A Belavin & V G Drinfel'd)
• Some Algebraic Structures Connected with the Yang-Baxter Equation (E K Sklyanin)
• Quantization of Lie Groups and Lie Algebras (L D Faddeev, N Yu Reshetikhin & L A Takhtajan)
• Families of Commuting Transfer Matrices in q-State Vertex Models in Non-Linear Integrable Systems — Classical Theory and Quantum Theory (J H H Perk & C L Schultz)
• Self-Dual Solutions of the Star-Triangle Relations in Z_N Models (V A Fateev & A B Zamolodchikov)
• Solvable Lattice Models Related to the Vector Representation of Classical Simple Lie Algebras (M Jimbo, T Miwa & M Okado)
• Exactly Solvable SOS Models. II: Proof of the Star-Triangle and Combinatorial Identities (E Date et al.)
• New Solutions of the Star-Triangle Relations for the Chiral Potts Model (R J Baxter, J H H Perk & H Au-Yang)
• and other papers