Integrals of vertex operators and quantum shuffles
Let \({\mathcal G}\) be a finite dimensional complex simple Lie algebra, \({\widehat {\mathcal G} }\) the corresponding affine Lie algebra, and \(U_q {n }_+\) the upper triangular part of the quantized enveloping algebra associated with \({\mathcal G}\). Then the integrals of vertex operators (i.e. the intertwining operators) on certain Fock modules for \({\widehat {\mathcal G} }\) satisfy the quantum Serre relations [cf. \textit{P. Bouwknegt, J. McCarthy}, and \textit{K. Pilch}, Commun. Math. Phys 131, 125-155 (1990; Zbl 0704.17009)]. In the paper under review the author gives an alternative proof of this result using the quantum shuffle construction of the `upper triangular part' \(U_q {n }_+\). He applies the general construction of representations of the quantum shuffle algebra built on a braided vector space.
scientific article; zbMATH DE number 1051422