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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.10340 |
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Table des matières:
- 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.