Higher spin polynomial solutions of quantum Knizhnik-Zamolodchikov equation (Q2248862)

Let \(q\neq 0\) be a complex number with \(|q|<1\) and denote by \(U = U_{q}(\widehat{\mathfrak{sl}_{2}})\) the quantized affine enveloping algebra of \(\mathfrak{sl}_{2}\). Using Drinfeld's realization of \(U\) in term of currents, the authors study correlation functions of (perfect) vertex operators associated to intertwiners of level \(\ell\) representations given by \(\ell\)-powers of a Fock space and evaluation representations of spin \(\ell/2\). As the main result it is shown, using explicit formulas, that these correlation functions are given by rational functions whose denominator is a Macdonald polynomial. Consequently, they satisfy a certain wheel condition. Finally, the authors apply the results to the computation of the ground state of higher spin vertex models, spin chains and loop models. The paper is well-written, well-organized and contains several appendices providing technical details, such as the construction of \(q\)-deformed parafermions and graphic calculus.