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- W2897780905 abstract "A bstract We introduce an R -matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $$ {U}_{q,t}left({widehat{widehat{mathfrak{gl}}}}_1right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:msub> <mml:mover> <mml:mover> <mml:mrow> <mml:mi>g</mml:mi> <mml:mi>l</mml:mi> </mml:mrow> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>^</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:mfenced> </mml:math> . 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 $$ frac{t}{q} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mfrac> <mml:mi>t</mml:mi> <mml:mi>q</mml:mi> </mml:mfrac> </mml:math> . 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." @default.
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- W2897780905 date "2019-04-01" @default.
- W2897780905 modified "2023-09-27" @default.
- W2897780905 title "The MacMahon R-matrix" @default.
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- W2897780905 doi "https://doi.org/10.1007/jhep04(2019)097" @default.
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