The Torus Centralizing Subalgebra of $\text{Dist}(G_r)$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917976518688768 |
|---|---|
| author | Sobaje, Paul |
| author_facet | Sobaje, Paul |
| contents | Let $G$ be a simple and simply connected algebraic group over a field of characteristic $p>0$, and $G_r$ its $r$-th Frobenius kernel. In this paper, we initiate a general study of $\text{Dist}(G_r)^T$, the subalgebra of $\text{Dist}(G_r)$ consisting of fixed points for the adjoint action of a maximal torus $T$ of $G$. We analyze the structure of this algebra, and classify its simple modules, which essentially are just the non-zero weight spaces of the simple $G_rT$-modules of $p^r$-restricted highest weight. Further connections between the representations of $\text{Dist}(G_r)^T$ and $G_rT$ are shown, demonstrating the potential usefulness of this algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Torus Centralizing Subalgebra of $\text{Dist}(G_r)$ Sobaje, Paul Representation Theory Let $G$ be a simple and simply connected algebraic group over a field of characteristic $p>0$, and $G_r$ its $r$-th Frobenius kernel. In this paper, we initiate a general study of $\text{Dist}(G_r)^T$, the subalgebra of $\text{Dist}(G_r)$ consisting of fixed points for the adjoint action of a maximal torus $T$ of $G$. We analyze the structure of this algebra, and classify its simple modules, which essentially are just the non-zero weight spaces of the simple $G_rT$-modules of $p^r$-restricted highest weight. Further connections between the representations of $\text{Dist}(G_r)^T$ and $G_rT$ are shown, demonstrating the potential usefulness of this algebra. |
| title | The Torus Centralizing Subalgebra of $\text{Dist}(G_r)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2504.03121 |