A Murnaghan-Nakayama rule for Grothendieck polynomials of Grassmannian type

TL;DR

This paper develops a Murnaghan-Nakayama rule for Grothendieck polynomials of Grassmannian type, enabling the expression of their products with power sum symmetric polynomials as linear combinations of similar polynomials.

Contribution

It introduces a new combinatorial rule for Grothendieck polynomials of Grassmannian type, extending classical symmetric function theory to K-theoretic contexts.

Findings

Established a Murnaghan-Nakayama rule for these Grothendieck polynomials.

Provided explicit formulas for product expansions with power sum symmetric polynomials.

Enhanced understanding of the algebraic structure of K-theoretic Schubert calculus.

Abstract

We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan-Nakayama rule for Grothendieck polynomials of the Grassmannian type. This rule allows us to express the product of a Grothendieck polynomial with a power sum symmetric polynomial into a linear combination of other Grothendieck polynomials.