Residues, Grothendieck polynomials and K-theoretic Thom polynomials

TL;DR

This paper introduces a new residue-based definition of double stable Grothendieck polynomials and applies it to compute K-theoretic Thom polynomials for A2 singularities, revealing their stabilization and finiteness properties.

Contribution

It provides a novel residue-based approach to define Grothendieck polynomials and demonstrates its effectiveness in calculating K-theoretic Thom polynomials for specific singularities.

Findings

Successful computation of K-theoretic Thom polynomials for A2 singularities

Demonstration of stabilization and finiteness properties in the expansions

New residue-based framework for Grothendieck polynomials

Abstract

Grothendieck polynomials were introduced by Lascoux and Sch\"utzenberger, and they 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 $A_2$ singularities. We present the expansion in two versions: one displays its expected stabilization, while the other displays its expected finiteness property.