Special functions, KZ type equations, and representation theory
著者
書誌事項
Special functions, KZ type equations, and representation theory
（Regional conference series in mathematics, no. 98）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society with support from the National Science Foundation, c2003
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注記
"CBMS Conference on Arrangements and Mathematical Physics, Louisiana State University, January 15-19, 2002"--T.p. verso
Includes bibliographical references (p. 109-115) and index
内容説明・目次
内容説明
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.
目次
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.
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