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A Local Characterization of Unions of Demazure Crystals (2512.19814v1)
Published 22 Dec 2025 in math.RT and math.CO
Abstract: We characterize subsets of highest weight $\mathfrak{g}$-crystals that arise as unions of Demazure crystals, for any symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$. We provide a local characterization for these subsets and prove they admit disjoint decompositions into Demazure atoms. As a consequence, we give a new characterization for when a subset of a highest weight crystal is a Demazure crystal as well as a crystal-theoretic proof that any Polo module admits a relative Schubert filtration.
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