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The integrability of 4d $\mathcal{N}=2$ gauge theories has been explored invarious contexts, for example the Seiberg-Witten curve and its quantization.Recently, Maulik and Okounkov proposed that an integrable lattice model isassociated with the gauge theory, through an R-matrix, to which we refer asMO's R-matrix in this paper, constructed in the instanton moduli space. In thispaper, we study the R-matrix using the Ding-Iohara-Miki (DIM) algebra. Weprovide a concrete boson realization of the universal R-matrix in DIM and showthat the defining conditions for MO's R-matrix can be derived from this freeboson oscillator expression. Several consistency checks for the oscillatorexpression are also performed.

Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra