The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its $q$-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions.

This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra $\mathfrak{sl}_2$.

This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.

Readership

Graduate students and research mathematicians interested in mathematical physics, in particular to those interested in application of special functions.

Reviews

"The book is a result of many years work and reading of lectures and, on my opinion, at this moment is the best exposition of the theory of KZ equations in which different facets and their connections are considered. It would be desirable to construct so complete the theory for the KZ equations associated to the other root systems."

-- Zentralblatt MATH

Table of Contents

• Hypergeometric solutions of KZ equations
• Cycles of integrals and the monodromy of the KZ equation
• Selberg integral, determinant formulas, and dynamical equations
• Critical points of master functions and the Bethe ansatz
• Elliptic hypergeometric functions
• q-hypergeometric solutions of qKZ equations
• Bibliography
• Index