Residues, Grothendieck Polynomials, and K-Theoretic Thom Polynomials

Abstract

Abstract Grothendieck polynomials were introduced by Lascoux and Schützenberger and play an important role in K-theoretic Schubert calculus. In this paper, we give a new definition of double stable Grothendieck polynomials based on an iterated residue operation. We illustrate the power of our definition by calculating the Grothendieck expansion of K-theoretic Thom polynomials of ${\mathcal {A}}_{2}$ singularities. We present this expansion in two versions: one displays its stabilization property, while the other displays its expected finiteness property.