**CBMS Regional Conference Series in Mathematics**

Volume: 85;
1995;
152 pp;
Softcover

MSC: Primary 17; 81; 82;

Print ISBN: 978-0-8218-0320-2

Product Code: CBMS/85

List Price: $25.00

Individual Price: $20.00

**Electronic ISBN: 978-1-4704-2445-9
Product Code: CBMS/85.E**

List Price: $25.00

Individual Price: $20.00

# Algebraic Analysis of Solvable Lattice Models

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*Michio Jimbo; Tetsuji Miwa*

A co-publication of the AMS and CBMS

Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin \(1/2\) XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the \(XXX\) model is briefly discussed, and the book closes with a discussion of other types of models and related works.

#### Readership

Advanced graduate students and researchers.

#### Reviews & Endorsements

The book provides a very clear exposition on the subject, and meanwhile gives an elementary introduction to representation theory … serves very well as both introduction and reference.

-- Mathematical Reviews

Very clearly written … suitable for those who may not be expert either in quantum groups or in the theory of solvable lattice models.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Algebraic Analysis of Solvable Lattice Models

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents ix10 free
- 0 Background of the problem 118 free
- 1 The spin 1/ 2 XXZ model for Δ < …1 1128
- 2 The six-vertex model in the anti-ferroelectric regime 1936
- 3 Solvability and Symmetry 2744
- 4 Correlation functions—physical derivation 4562
- 5 Level one modules and bosonization 6380
- 6 Vertex operators 7188
- 7 Space of states—mathematical picture 83100
- 8 Traces of vertex operators 93110
- 9 Correlation functions and form factors 109126
- 10 The XXX limit q —> –1 119136
- 11 Discussions 127144
- A List of formulas 141158
- Back Cover 163180