A Local Characterization of Unions of Demazure Crystals

Fuente: arXiv
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Main Authors: Assaf, Sami, González, Nicolle
Format: Preprint
Published: 2025
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author Assaf, Sami
González, Nicolle
author_facet Assaf, Sami
González, Nicolle
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_19814
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Local Characterization of Unions of Demazure Crystals
Assaf, Sami
González, Nicolle
Representation Theory
Combinatorics
17B37, 05E10, 20G42
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.
title A Local Characterization of Unions of Demazure Crystals
topic Representation Theory
Combinatorics
17B37, 05E10, 20G42
url https://arxiv.org/abs/2512.19814