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We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W_{1+infty} introduced by Miki.
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A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex , J. High Energy Phys. (2009) no. 10, 069, 58pp
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L.F. Alday, D. Gaiotto, Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories , Lett. Math. Phys. 91
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H. Awata, Y. Yamada, Five-dimensional AGT Conjecture and the Deformed Virasoro algebra , JHEP 1001:125 (2010)
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A. Iqbal, All genus topological string amplitudes and 5-brane webs as Feynman diagrams , hep-th/0207114
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B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin, Quantum continuous 𝔤 𝔩 ∞ \mathfrak{gl}_{\infty} , Tensor products of Fock modules and W n W_{n} characters , Kyoto J. Math. 51
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O. Schiffmann, E. Vasserot, The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials , Compos, Math. 147
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