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arXiv · 2512.19814

A Local Characterization of Unions of Demazure Crystals

Sami Assaf·Nicolle González
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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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Sami Assaf, Nicolle González. 2025-12-22. A Local Characterization of Unions of Demazure Crystals. https://arxiv.org/abs/2512.19814

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