On Mirković-Vilonen polytopes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909077173436416 |
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| author | Baumann, Pierre |
| author_facet | Baumann, Pierre |
| contents | Mirković-Vilonen polytopes encode in a geometrical way the numerical data present in the Kashiwara crystal $B(\infty)$ of a semisimple group $G$. We retrieve these polytopes from the coproduct of the Hopf algebra $\mathscr O(N)$ of regular functions on a maximal unipotent subgroup $N$ of $G$. We bring attention to a remarkable behavior that the classical bases (dual canonical, dual semicanonical, Mirković-Vilonen) of $\mathscr O(N)$ manifest with respect to the extremal points of these polytopes, which extends the crystal operations. This study leans on a notion of stability for graded bialgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Mirković-Vilonen polytopes Baumann, Pierre Representation Theory 22E46 (Primary) 14M15 (Secondary) Mirković-Vilonen polytopes encode in a geometrical way the numerical data present in the Kashiwara crystal $B(\infty)$ of a semisimple group $G$. We retrieve these polytopes from the coproduct of the Hopf algebra $\mathscr O(N)$ of regular functions on a maximal unipotent subgroup $N$ of $G$. We bring attention to a remarkable behavior that the classical bases (dual canonical, dual semicanonical, Mirković-Vilonen) of $\mathscr O(N)$ manifest with respect to the extremal points of these polytopes, which extends the crystal operations. This study leans on a notion of stability for graded bialgebras. |
| title | On Mirković-Vilonen polytopes |
| topic | Representation Theory 22E46 (Primary) 14M15 (Secondary) |
| url | https://arxiv.org/abs/2401.10340 |