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The MacMahon R-matrix

  • Hidetoshi Awata
  • Hiroaki Kanno
  • Andrei MironovEmail author
  • Alexei Morozov
  • Kazuma Suetake
  • Yegor Zenkevich
Open Access
Regular Article - Theoretical Physics
  • 20 Downloads

Abstract

We introduce an R-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra \( {U}_{q,t}\left({\widehat{\widehat{\mathfrak{gl}}}}_1\right) \). 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.

Keywords

Conformal and W Symmetry Quantum Groups Topological Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Hidetoshi Awata
    • 1
  • Hiroaki Kanno
    • 1
    • 2
  • Andrei Mironov
    • 3
    • 4
    • 5
    Email author
  • Alexei Morozov
    • 4
    • 5
  • Kazuma Suetake
    • 1
  • Yegor Zenkevich
    • 4
    • 6
    • 7
  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  2. 2.KMINagoya UniversityNagoyaJapan
  3. 3.Theory DepartmentLebedev Physics InstituteMoscowRussia
  4. 4.ITEPMoscowRussia
  5. 5.Institute for Information Transmission ProblemsMoscowRussia
  6. 6.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly
  7. 7.INFN, sezione di Milano-BicoccaMilanoItaly

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