Operator Product Formulas in the Algebraic Approach of the Refined Topological Vertex

The refined topological vertex of Iqbal–Koz?az–Vafa has been investigated from the viewpoint of the quantum algebra of type W_1+∞ by Awata, Feigin, and Shiraishi. They introduced the trivalent intertwining operator ? which is normal ordered along with some prefactors. We manage to establish formulas from the infinite operator product of the vertex operators and the generalized ones to restore this prefactor, and obtain an explicit formula for the vertex realization of the topological vertex as well as the refined topological vertex.