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

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

  1. 384 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

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

About this book

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.

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Yes, you can access Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups by Alexander Varchenko in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Contents
  2. 1. Introduction
  3. 2. Construction of complexes calculating homology of the complement of a configuration
  4. 3. Construction of homology complexes for discriminantal configuration
  5. 4. Algebraic interpretation of chain complexes of a discriminantal configuration
  6. 5. Quasiisomorphism of two-sided Hochschild complexes to suitable one-sided Hochschild complexes
  7. 6. Bundle properties of a discriminantal configuration
  8. 7. R-matrix for the two-sided Hochschild complexes
  9. 8. Monodromy
  10. 9. R-matrix operator as the canonical element quantum doubles
  11. 10. Hypergeometric integrals
  12. 11. Kac-Moody Lie algebras without Serre's relations and their doubles
  13. 12. Hypergeometric integrals of a discriminantal configuration
  14. 13. Resonances at infinity
  15. 14. Degenerations of discriminantal configurations
  16. 15. Remarks on homology groups of a configuration with coefficients in local systems more general than complex one-dimensional
  17. References