The MacMahon R-matrix

2018/10/31 by H. Awata, H. Kanno, A. Mironov +3 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.QA #math.RT

paper · pdf · doi:10.1007/jhep04(2019)097

published as JHEP 2019 (2019) 97 · 39 pages

arxiv created 2019/04/20 · arxiv updated 2019/04/23

Abstract

We introduce an R-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra U_q,t(\widehat\widehat\mathfrakgl₁). This R-matrix acts on pairs of 3d 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.

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