Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 General Overview of Multivariable Special Functions
- 2 Orthogonal Polynomials of Several Variables
- 3 Appell and Lauricella Hypergeometric Functions
- 4 A-Hypergeometric Functions
- 5 Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
- 6 Elliptic Hypergeometric Functions Associated with Root Systems
- 7 Dunkl Operators and Related Special Functions
- 8 Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
- 9 Macdonald–Koornwinder Polynomials
- 10 Combinatorial Aspects of Macdonald and Related Polynomials
- 11 Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
- 12 9 j-Coefficients and Higher
- Index
11 - Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
Published online by Cambridge University Press: 30 September 2020
Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 General Overview of Multivariable Special Functions
- 2 Orthogonal Polynomials of Several Variables
- 3 Appell and Lauricella Hypergeometric Functions
- 4 A-Hypergeometric Functions
- 5 Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems
- 6 Elliptic Hypergeometric Functions Associated with Root Systems
- 7 Dunkl Operators and Related Special Functions
- 8 Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems
- 9 Macdonald–Koornwinder Polynomials
- 10 Combinatorial Aspects of Macdonald and Related Polynomials
- 11 Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
- 12 9 j-Coefficients and Higher
- Index
Summary
The KZ equations are a fundamental mathematical structure related to hypergeometric functions. Solutions of all versions of KZ equations are given by multidimensional hypergeometric integrals. The semi-classical limit of KZ equations leads to basic quantum chain models of mathematical physics and representation theory. In this chapter we describe the main examples of the KZ equations (rational, trigonometric, elliptic, differential or difference) with integral hypergeometric solutions. We also describe the semi-classical limit of KZ equations and associated Bethe ansatz method as the semi-classical limit of the hypergeometric solutions.
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- Encyclopedia of Special Functions: The Askey-Bateman Project , pp. 368 - 401Publisher: Cambridge University PressPrint publication year: 2020
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