INTEGRALS OF VERTEX OPERATORS AND QUANTUM SHUFFLES

Given a braided vector space (V, sigma), we show that iterated integra ls of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on (V, sigma). Using the quantum shuffle construction of the 'upper tri a ngular part' U(q)n(+) of a quantized enveloping algebra, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules giv e rise to representations of U(q)n(+).