A Littlewood-Richardson Rule for Dual Stable Grothendieck Polynomials

TL;DR

This paper extends the Littlewood-Richardson rule to dual stable Grothendieck polynomials by constructing a crystal graph on reverse plane partitions, providing a combinatorial tool for polynomial expansion.

Contribution

It introduces a crystal graph framework for reverse plane partitions to generalize the Littlewood-Richardson rule for dual stable Grothendieck polynomials.

Findings

Crystal graph construction on reverse plane partitions

Extended Littlewood-Richardson rule for dual stable Grothendieck polynomials

Simplified expansion in terms of Schur polynomials

Abstract

For a given skew shape, we build a crystal graph on the set of all reverse plane partitions that have this shape. As a consequence, we get a simple extension of the Littlewood-Richardson rule for the expansion of the corresponding dual stable Grothendieck polynomial in terms of Schur polynomials.