Demazure crystal structure for flagged reverse plane partitions

TL;DR

This paper demonstrates that flagged reverse plane partitions form a union of Demazure crystals, leading to the key positivity of flagged dual stable Grothendieck polynomials, thus connecting combinatorial structures with algebraic representations.

Contribution

It establishes a crystal-theoretic structure for flagged reverse plane partitions and proves key positivity of associated polynomials, advancing combinatorial and algebraic understanding.

Findings

Flagged reverse plane partitions form a disjoint union of Demazure crystals.

Flagged dual stable Grothendieck polynomials are key positive.

Provides a crystal-theoretic interpretation of flagged combinatorial objects.

Abstract

Given a skew shape $ \lambda / \mu $ and a flag $\Phi,$ we show that the set of all flagged reverse plane partitions of shape $\lambda / \mu$ and flag $\Phi$ is a disjoint union of Demazure crystals (up to isomorphism). As a result, the flagged dual stable Grothendieck polynomial $ g_{\lambda/\mu}(X_\Phi)$ is shown to be key positive.