Quantum affine algebras and holonomic difference equations
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.
\(q\)-analogue of Knizhnik-Zamolodchikov equation
elliptic solutions of Yang-Baxter equations
\(q\)-analogue of conformal field theory
representations of quantum affine algebras
scientific article; zbMATH DE number 61993
scientific article