Wreath Macdonald polynomials as eigenstates

• Joshua Jeishing Wen ^[1]
  1. [1] University of Vienna

     University of Vienna

     Innere Stadt, Austria

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01059-0
• Enlaces
  • Texto completo
• Resumen

  • We show that the wreath Macdonald polynomials forZ/Zn, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra Uq,d( ¨ sl), diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials.

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