A Local Characterization of Unions of Demazure Crystals
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918259704463360 |
|---|---|
| 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 |