The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908421368840192 |
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| author | Chen, Xiaoyu Dong, Junbin |
| author_facet | Chen, Xiaoyu Dong, Junbin |
| contents | Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements. Let $\Bbbk$ be a field such that $\op{char} \Bbbk \ne \op{char} \mathbb{F}_q$. In this paper, we study the extensions of simple modules (over $\Bbbk$) in the principal representation category $\mathscr{O}(\bf G)$ which is defined in \cite{D1}. In particular, we get the block decomposition of $\mathscr{O}(\bf G)$, which is parameterized by the central characters of ${\bf G}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps Chen, Xiaoyu Dong, Junbin Representation Theory Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements. Let $\Bbbk$ be a field such that $\op{char} \Bbbk \ne \op{char} \mathbb{F}_q$. In this paper, we study the extensions of simple modules (over $\Bbbk$) in the principal representation category $\mathscr{O}(\bf G)$ which is defined in \cite{D1}. In particular, we get the block decomposition of $\mathscr{O}(\bf G)$, which is parameterized by the central characters of ${\bf G}$. |
| title | The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2506.20378 |