Duality and deformations of stable Grothendieck polynomials

TL;DR

This paper introduces a two-parameter extension of stable Grothendieck polynomials, called canonical stable Grothendieck functions, exploring their algebraic, combinatorial, and duality properties within K-theory.

Contribution

It defines and analyzes canonical stable Grothendieck functions, revealing their structure constants, self-duality, and combinatorial identities, expanding the understanding of K-theoretic symmetric functions.

Findings

Same structure constants as original polynomials (up to scaling)

Self-duality under ring automorphism

Derived combinatorial and algebraic identities

Abstract

Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonical stable Grothendieck functions. These functions have the same structure constants (with scaling) as stable Grothendieck polynomials, and (composing with parameter switching) are self-dual under the standard involutive ring automorphism. We study various properties of these functions, including combinatorial formulas, Schur expansions, Jacobi-Trudi type identities, and associated Fomin-Greene operators.