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arXiv · 1810.07676

The MacMahon R-matrix

H. Awata·H. Kanno·A. Mironov·A. Morozov·K. Suetake·Y. Zenkevich
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Abstract

We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. 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 $\frac{t}{q}$. 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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H. Awata, H. Kanno, A. Mironov, A. Morozov, K. Suetake, Y. Zenkevich. 2018-10-17. The MacMahon R-matrix. https://doi.org/10.1007/jhep04(2019)097

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