Key expansion of the flagged refined skew stable Grothendieck polynomial

TL;DR

This paper develops a combinatorial expansion of flagged refined skew stable Grothendieck polynomials using Demazure crystal structures, connecting them to key polynomials and other symmetric functions.

Contribution

It introduces a new combinatorial framework for expanding flagged refined skew stable Grothendieck polynomials via Demazure crystals, linking them to key polynomials.

Findings

Demazure crystal structure on flagged tableaux

Expansion of flagged refined skew stable Grothendieck polynomials in terms of key polynomials

Connections to stable and dual stable Grothendieck polynomials

Abstract

The flagged refined stable Grothendieck polynomials of skew shapes generalize several polynomials like stable Grothendieck polynomials, flagged skew Schur polynomials. In this paper, we provide a combinatorial expansion of the flagged refined skew stable Grothendieck polynomial in terms of key polynomials. We present this expansion by imposing a Demazure crystal structure on the set of flagged semi-standard set-valued tableaux of a given skew shape and a flag. We also provide expansions of the row-refined stable Grothendieck polynomials and refined dual stable Grothendieck polynomials and the Schur P-functions in terms of stable Grothendieck polynomials $G_{\lambda}$ and in terms of dual stable Grothendieck polynomials $g_{\lambda}$.