Notes on Schubert, Grothendieck and Key Polynomials

TL;DR

This paper introduces a unified framework for various classes of polynomials related to algebraic combinatorics, based on the study of the reduced rectangular plactic algebra and Cauchy kernels.

Contribution

It provides a common generalization of multiple polynomial families, connecting algebraic and combinatorial properties through the reduced rectangular plactic algebra.

Findings

Unified algebraic framework for Schubert, Grothendieck, and related polynomials

New combinatorial interpretations via reduced rectangular plactic algebra

Enhanced understanding of polynomial interrelations and properties

Abstract

We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco-Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.