On local integrability results for $p$-adic reductive groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918450677415936 |
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| author | Tsai, Cheng-Chiang |
| author_facet | Tsai, Cheng-Chiang |
| contents | We present a short proof, based on local character expansions, of the celebrated theorem of Harish-Chandra about local integrability of complex characters of $p$-adic reductive groups. The proof gives an algebraic incarnation of the local integrability that works for some coefficients different from $\mathbb{C}$, verifies local integrability in cases that appear not covered in the literature, and shows that a character is locally-$L^α$ for some specified $α>1$ as in [GGH23]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15079 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On local integrability results for $p$-adic reductive groups Tsai, Cheng-Chiang Representation Theory Number Theory We present a short proof, based on local character expansions, of the celebrated theorem of Harish-Chandra about local integrability of complex characters of $p$-adic reductive groups. The proof gives an algebraic incarnation of the local integrability that works for some coefficients different from $\mathbb{C}$, verifies local integrability in cases that appear not covered in the literature, and shows that a character is locally-$L^α$ for some specified $α>1$ as in [GGH23]. |
| title | On local integrability results for $p$-adic reductive groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2604.15079 |