The MacMahon R-matrix

A bstract We introduce an R -matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra U q , t g l ^ ^ 1 . This R -matrix acts on pairs of 3 d Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters q , t −1 and t q . We construct the intertwining operator for a tensor product of the horizontal Fock representation and the vertical MacMahon representation and show that the intertwiners are permuted using the MacMahon R -matrix.