Quantum Groups in Two-Dimensional Physics (original) (raw)

Preface xv 1 S-matrices, spin chains and vertex models 1 1.1 Factorized S-matrix models 1 1.1.1 Zamolodchikov algebra 5 1.1.2 Example 7 1.2 Bethe's diagonalization of spin chain hamiltonians 1.3 Integrable vertex models: the six-vertex model Exercises 25 Appendix A Form factors ' 28 Al.l Introduction to Smirnov's program 28 A1.2 Form factors at work: the Ising model Exercise 2 The Yang-Baxter equation: a first look 2.1 The Yang-Baxter algebra 2.1.1 The 52-matrix and the Yang-Baxter equation 2.1.2 The monodromy matrix 2.1.3 Co-product and the Yang-Baxter algebra 39 2.1.4 Algebraic Bethe ansatz 2.2 Yang-Baxter algebras and braid groups 2.3 Yang-Baxter algebras and quantum groups = 51 2.3.1 The ^-matrix as an intertwiner 2.3.2 A first contact with affine Hopf algebras 2.4 Descendants of the six-vertex model 2.4.1 Descent procedure 2.4.2 Bethe ansatz for descendant models 2.5 Comments 2.5.1 Explanation of our conventions 2.5.2 On parametrizations of the six-vertex weights Exercises ^ 3 Bethe ansatz: some examples 3.1 Introduction and summary 3.2 The phase structure of the six-vertex model