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Kirillov’s Conjecture on Hecke–Grothendieck Polynomials

Year: 2025
Type: article
Abstract: We use algebraic methods in statistical mechanics to represent a multi-parameter class of polynomials in several variables as partition functions of a new family of solvable lattice models. The class of polynomials, defined by A. N. Kirillov, is derived from the largest class of divided difference operators satisfying the braid relations of Cartan type $A$. It includes as specializations Schubert, Grothendieck, and dual-Grothendieck polynomials, among others. In particular, our results prove positivity conjectures of Kirillov for the subfamily of Hecke–Grothendieck polynomials, while the larger family is shown to exhibit rare instances of negative coefficients.
DOI: 10.1093/imrn/rnaf380
Authors: Ben Brubaker, A Suki Dasher, Michael Hu, Nupur Jain, Yifan Li, Yi Lin, Maria Mihaila, Van Tran, I Deniz Ünel
Institutions: University of Minnesota, University of Illinois Urbana-Champaign, Ruhr University Bochum, University of Southern California, The Ohio State University, Vanderbilt University, Case Western Reserve University, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Open Access status: green
OpenAlex ID: W7124681514
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Cites: 28
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