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Article Dans Une Revue Selecta Mathematica (New Series) Année : 2022

Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials

Jim Haglund
  • Fonction : Auteur
Olya Mandelshtam
  • Fonction : Auteur
Sarah Mason
  • Fonction : Auteur
Lauren Williams
  • Fonction : Auteur

Résumé

Abstract We describe a novel Yang–Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are essentially equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model formalism, we give alternate proofs of many properties of these polynomials, including symmetry and a Cauchy identity.

Dates et versions

hal-03875134 , version 1 (28-11-2022)

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Citer

Sylvie Corteel, Jim Haglund, Olya Mandelshtam, Sarah Mason, Lauren Williams. Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials. Selecta Mathematica (New Series), 2022, 28 (2), pp.32. ⟨10.1007/s00029-021-00721-7⟩. ⟨hal-03875134⟩

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