CBMS Regional Conference Series in Mathematics 2003; 118 pp; softcover Number: 98 ISBN10: 0821828673 ISBN13: 9780821828670 List Price: US$41 Member Price: US$32.80 All Individuals: US$32.80 Order Code: CBMS/98
 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 KnizhnikZamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multidimensional 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
 qhypergeometric solutions of qKZ equations
 Bibliography
 Index
