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