Free boson representation of \(q\)-vertex operators and their correlation functions (Q1311696)

A bosonization scheme of the \(q\)-vertex operators of the quantized algebra \(U_ q (\widehat {{\mathfrak sl}_ 2})\) for arbitrary level is proposed. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. As a consequence, \(N\)-point correlation functions for these vertex operators are presented in the form of a Jackson integral. The properties of the two-point correlation functions are discussed in more detail, including the defining system of \(q\)-difference Knizhnik-Zamolodchikov equations.