Lanterna Rally

Author: A Varchenko

Publisher: World Scientific

Published: 1995-03-29

Total Pages: 384

ISBN-13: 981450162X

This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik–Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals. Contents:IntroductionConstruction of Complexes Calculating Homology of the Complement of a ConfigurationConstruction of Homology Complexes for Discriminantal ConfigurationAlgebraic Interpretation of Chain Complexes of a Discriminantal ConfigurationQuasiisomorphism of Two-Sided Hochschild Complexes to Suitable One-Sided Hochschild ComplexesBundle Properties of a Discriminantal ConfigurationR-Matrix for the Two-Sided Hochschild ComplexesMonodromyR-Matrix Operator as the Canonical Element, Quantum DoublesHypergeometric IntegralsKac–Moody Lie Algebras Without Serre's Relations and Their DoublesHypergeometric Integrals of a Discriminantal ConfigurationResonances at InfinityDegenerations of Discriminantal ConfigurationsRemarks on Homology Groups of a Configuration with Coefficients in Local Systems More General than Complex One-Dimensional Readership: Mathematicians, theoretical physicists, and graduate students. keywords:Hypergeometric Function;Hypergeometric Type Function;Hypergeometric Integral;Kac-Moody Algebra;Quantum Group;Representations of a Kac-Moody Algebra;Representations of a Quantum Group;Discriminant Configuration;Monodromy “The book is elegantly structured and sticks closely to the point, and is also fairly down to earth … as well as serving as an excellent specialist monograph, it should also be useful as a first exposure to these topics for anyone who likes to learn a subject through the study of a concrete problem.” Bull. London Math. Soc.