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Journal Articles Selecta Mathematica (New Series) Year : 2022

Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials

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Jim Haglund
  • Function : Author
Olya Mandelshtam
  • Function : Author
Sarah Mason
  • Function : Author
Lauren Williams
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Abstract

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 and versions

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

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Cite

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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