Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III

Two-Dimensional Ising Model

Monodromy preserving deformation of linear ordinary differential equations with rational coefficients: I. General theory and τ-function

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Toda lattice hierarchy

As a continuation of previous work, discretization of nonlinear Schrodinger equation and its analogues are discussed as the reduction of 2-component KP hierarchy

Method for Generating Discrete Soliton Equation. III

The notion of solitons arose with the study of partial differential equations at the end of the 19th century. In more recent times their study has involved ideas from other areas of mathematics such as algebraic gometry, topology, and in particular infinite dimensional Lie algebras, and it this approach that is the main theme of this book.This book will be of great interest to all whose research interests involves the mathematics of solitons.

Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras

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Studies on holonomic quantum fields, XVII

We discuss a construction of highest weight modules for the recently defined elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, and make several conjectures concerning them. The modules are generated by the action of the components of the operator $L$ on the highest weight vectors. We introduce the vertex operators $\Phi$ and $\Psi^*$ through their commutation relations with the $L$-operator. We present ordering rules for the $L$- and $\Phi$-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of $\widehat{sl}_2$-modules.

Michio Jimbo

Papers

Method for Generating Discrete Soliton Equation. III

Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras

Studies on holonomic quantum fields, XVII

Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}\left(\widehat{sl}_2\right)$

Transformation groups for soliton equations. 6. kp hierarchies of orthogonal and symplectic type