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multidimensional hypergeometric integrals

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11 - Knizhnik–Zamolodchikov-Type Equations, Selberg Integrals and Related Special Functions
- By V. Tarasov, A. Varchenko
Edited by Tom H. Koornwinder, Universiteit van Amsterdam, Jasper V. Stokman, Universiteit van Amsterdam
Book:

Encyclopedia of Special Functions: The Askey-Bateman Project

Published online:

30 September 2020

Print publication:

15 October 2020, pp 368-401
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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.