Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups

Download or read book Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups written by Alexander Varchenko and published by World Scientific. This book was released on 1995-03-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.