Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.10340 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.