Quantum affine algebras and holonomic difference equations
type: Item
instance of: scholarly article
title: Quantum affine algebras and holonomic difference equations
zbMATH Open document ID: 0760.17006
DOI: 10.1007/BF02099206
published in: Communications in Mathematical Physics
publication date: 1992-09-27T00:00:00Z
review text: This paper initiates the study of a \(q\)-analogue of conformal field theory (CFT). In classical CFT, a fundamental role is played by the Knizhnik-Zamolodchikov (KZ) equation, which is satisfied by the matrix elements of intertwiners between tensor products of certain representations of affine Lie algebras. The solutions of the KZ equation can be expressed in terms of hypergeometric functions and their generalizations. The authors introduce a \(q\)-analogue of the KZ equation, show its relation to representations of quantum affine algebras, and express its solutions in terms of \(q\)-hypergeometric functions.
reviewed by: Andrew N. Pressley
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 61993
zbMATH Keywords: \(q\)-analogue of Knizhnik-Zamolodchikov equation
zbMATH Keywords: holonomic \(q\)-difference equations
zbMATH Keywords: matrix coefficients
zbMATH Keywords: intertwining operators
zbMATH Keywords: connection operators
zbMATH Keywords: elliptic solutions of Yang-Baxter equations
zbMATH Keywords: \(q\)-analogue of conformal field theory
zbMATH Keywords: representations of quantum affine algebras
zbMATH Keywords: \(q\)- hypergeometric functions
Wikidata QID: Q56687377
author: Igor B. Frenkel
author: Nicolai Reshetikhin
MaRDI profile type: Publication
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Quantum affine algebras and holonomic difference equations (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02099206

Quantum affine algebras and holonomic difference equations (OpenAlex ID)
OpenAlex ID: W1994253047