Demazure crystal structure for flagged reverse plane partitions

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.

10 pages, rewritten Sections 2.2, 3.2 & 5, added references, fixed typos