Resumen de Refined dual Grothendieck polynomials, integrability, and the Schur measure

Kohei Motegi, Travis Scrimshaw

• 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.