Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911320673091584 |
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| author | Taylor, James |
| author_facet | Taylor, James |
| contents | For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of $D^\times$ on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of $D^\times$ to $G^0$-finite $\text{GL}_n(F)$-equivariant vector bundles with connection on $Ω$, the $(n-1)$-dimensional Drinfeld symmetric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces Taylor, James Number Theory Representation Theory For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of $D^\times$ on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of $D^\times$ to $G^0$-finite $\text{GL}_n(F)$-equivariant vector bundles with connection on $Ω$, the $(n-1)$-dimensional Drinfeld symmetric space. |
| title | Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2406.14543 |