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Abstract A brane construction of an integrable lattice model is proposed. The model is composed of Belavin’s R-matrix, Felder’s dynamical R-matrix, the Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining operators. This construction implies that a family of surface defects act on supersymmetric indices of four-dimensional N $$ \mathcal{N} $$ = 1supersymmetricfieldtheoriesastransfermatricesrelatedtoellipticquantumgroups.