Local character expansion for mod-$\ell$ representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911228272574464 |
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| author | Tsai, Cheng-Chiang |
| author_facet | Tsai, Cheng-Chiang |
| contents | Let $G$ be a $p$-adic reductive group with $p$ ``very large.'' For any irreducible admissible representation $π$ of $G$ over an algebraically closed field $C$ of characteristic $\not=p$, we define a ``local character expansion'' of $π$ with coefficients $c_{\mathcal{O}}(π)\in\mathbb{Q}$, that does not use the character of $π$ directly but instead use the multiplicities of degenerate Moy-Prasad types. Note that the existence of local character expansion for mod-$\ell$ representations is shown by another paper of the author using a different and quicker method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local character expansion for mod-$\ell$ representations Tsai, Cheng-Chiang Representation Theory Number Theory Let $G$ be a $p$-adic reductive group with $p$ ``very large.'' For any irreducible admissible representation $π$ of $G$ over an algebraically closed field $C$ of characteristic $\not=p$, we define a ``local character expansion'' of $π$ with coefficients $c_{\mathcal{O}}(π)\in\mathbb{Q}$, that does not use the character of $π$ directly but instead use the multiplicities of degenerate Moy-Prasad types. Note that the existence of local character expansion for mod-$\ell$ representations is shown by another paper of the author using a different and quicker method. |
| title | Local character expansion for mod-$\ell$ representations |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2510.20510 |