An application of Aomoto-Gelfand hypergeometric functions to the SU(n) Knizhnik-Zamolodchikov equation (Q750691)

This article gives an explicit integral representation of the n-point functions of the SU(n) Wess-Zumino-Witten model as solutions to the Knizhnik-Zamolodchikov equation, which is a special class of Aomoto- Gelfand generalized hypergeometric differential equations. This generalizes former works of Christe-Flume, Zamolodchikov-Fateev or Date- Jimbo-Matsuo-Miwa made for \(n=2\). The author employs expressions via Verma modules of the Lie algebra \(sl(n+1,{\mathbb{C}})\). It is reported that Schechtman-Varchenko independently treated general symmetrizable Kac- Moody Lie algebra using different expressions.