Key expansion of the flagged refined skew stable Grothendieck polynomial

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 in terms of stable Grothendieck polynomials $G_{\lambda}$ and in terms of dual stable Grothendieck polynomials $g_{\lambda}$.