Orbital integral bounds the character for cuspidal representations of $GL_n(\mathbb{F}_{\ell}((t)))$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914336769835008 |
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| author | Aizenbud, Avraham Gourevitch, Dmitry Kazhdan, David Sayag, Eitan |
| author_facet | Aizenbud, Avraham Gourevitch, Dmitry Kazhdan, David Sayag, Eitan |
| contents | We prove that the character of an irreducible cuspidal representation of $GL_n(\mathbb{F}_{\ell}((t)))$ is locally bounded up to a logarithmic factor by the orbital integral of a matrix coefficient of this representation.
The characteristic $0$ analog of this result is part of the proof of the celebrated Harish-Chandra's integrability theorem.
In a sequel work [AGKS] we use this result in order to prove a positive characteristic analog of Harish-Chandra's integrability theorem under some additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16393 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbital integral bounds the character for cuspidal representations of $GL_n(\mathbb{F}_{\ell}((t)))$ Aizenbud, Avraham Gourevitch, Dmitry Kazhdan, David Sayag, Eitan Representation Theory 14L99, 20G25, 28C15, 28C05 We prove that the character of an irreducible cuspidal representation of $GL_n(\mathbb{F}_{\ell}((t)))$ is locally bounded up to a logarithmic factor by the orbital integral of a matrix coefficient of this representation. The characteristic $0$ analog of this result is part of the proof of the celebrated Harish-Chandra's integrability theorem. In a sequel work [AGKS] we use this result in order to prove a positive characteristic analog of Harish-Chandra's integrability theorem under some additional assumptions. |
| title | Orbital integral bounds the character for cuspidal representations of $GL_n(\mathbb{F}_{\ell}((t)))$ |
| topic | Representation Theory 14L99, 20G25, 28C15, 28C05 |
| url | https://arxiv.org/abs/2602.16393 |