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Refined dual Grothendieck polynomials, integrability, and the Schur measure

  • Kohei Motegi [1] ; Travis Scrimshaw [2]
    1. [1] Tokyo University of Marine Science and Technology

      Tokyo University of Marine Science and Technology

      Japón

    2. [2] Hokkaido University

      Hokkaido University

      Chūō-ku, Japón

  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-025-01041-w
  • Enlaces
  • Resumen

    • We investigate relations between refined dual Grothendieck polynomials, integrable lattice models, and stochastic processes. We first construct a vertex model whose partition function is a refined dual Grothendieck polynomial, where the states are interpreted as nonintersecting lattice paths. Using this, we show refined dual Grothendieck polynomials are multi-Schur functions and give a number of identities, including a Littlewood and Cauchy(–Littlewood) identity. We show that dual Grothendieck polynomials (up to a normalizing factor) describe the transition probabilities for the last passage percolation (LPP) random matrix process by refining a connection first noticed by Yeliussizov. By refining algebraic techniques of Johansson, we show Jacobi–Trudi formulas for skew refined dual Grothendieck polynomials conjectured by Grinberg and recover a relation between LPP and the Schur process due to Baik and Rains. Lastly, we extend our vertex model techniques to show some identities for refined Grothendieck polynomials, including a Jacobi–Trudi formula.

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