Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials

• Sylvie Corteel ^[5] ; Jim Haglund ^[1] ; Olya Mandelshtam ^[2] ; Sarah Mason ^[3] ; Lauren Williams ^[4]
  1. [1] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
  2. [2] University of Waterloo

     University of Waterloo

     Canadá

     
  3. [3] Wake Forest University

     Wake Forest University

     Township of Winston, Estados Unidos

     
  4. [4] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  5. [5] UC Berkeley, USA

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• DOI: 10.1007/s00029-021-00721-7
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact “multiline queue” formula for Macdonald polynomials due to Corteel, Mandelshtam, and Williams. We also introduce a new quasisymmetric analogue of Macdonald polynomials. These “quasisymmetric Macdonald polynomials" refine the (symmetric) Macdonald polynomials and specialize to the quasisymmetric Schur polynomials defined by Haglund, Luoto, Mason, and van Willigenburg.