Integrals of vertex operators and quantum shuffles
type: Item
instance of: scholarly article
title: Integrals of vertex operators and quantum shuffles
zbMATH Open document ID: 0896.17006
DOI: 10.1023/A:1007352917712
author: Marc Rosso
published in: Letters in Mathematical Physics
publication date: 1998-09-26T00:00:00Z
review text: 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.
reviewed by: Dražen Adamović
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1051422
zbMATH Keywords: quantized enveloping algebras
zbMATH Keywords: vertex operators
zbMATH Keywords: iterated integrals
zbMATH Keywords: upper triangular part
zbMATH Keywords: intertwining operators
zbMATH Keywords: quantum Serre relations
zbMATH Keywords: quantum shuffle
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1051422