Abstract
Given a braided vector space \(\left( {V,\sigma } \right)\) , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on \(\left( {V,\sigma } \right)\). Using the quantum shuffle construction of the 'upper triangular part' \(U_q n_{\text{ + }}\) of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of \(U_q n_{\text{ + }}\).
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Rosso, M. Integrals of Vertex Operators and uantum Shuffles. Letters in Mathematical Physics 41, 161–168 (1997). https://doi.org/10.1023/A:1007352917712
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DOI: https://doi.org/10.1023/A:1007352917712