Simple supercuspidal L-packets of split special orthogonal groups over dyadic fields
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909645316030464 |
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| author | Adrian, Moshe Henniart, Guy Kaplan, Eyal Oi, Masao |
| author_facet | Adrian, Moshe Henniart, Guy Kaplan, Eyal Oi, Masao |
| contents | We consider the split special orthogonal group $\mathrm{SO}_{N}$ defined over a $p$-adic field. We determine the structure of any $L$-packet of $\mathrm{SO}_{N}$ containing a simple supercuspidal representation (in the sense of Gross--Reeder). We also determine its endoscopic lift to a general linear group. Combined with the explicit local Langlands correspondence for simple supercuspidal representations of general linear groups, this leads us to get an explicit description of the $L$-parameter as a representation of the Weil group of $F$. Our result is new when $p=2$ and our method provides a new proof even when $p\neq2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09076 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simple supercuspidal L-packets of split special orthogonal groups over dyadic fields Adrian, Moshe Henniart, Guy Kaplan, Eyal Oi, Masao Number Theory Representation Theory 22E50, 11F70, 11L05 We consider the split special orthogonal group $\mathrm{SO}_{N}$ defined over a $p$-adic field. We determine the structure of any $L$-packet of $\mathrm{SO}_{N}$ containing a simple supercuspidal representation (in the sense of Gross--Reeder). We also determine its endoscopic lift to a general linear group. Combined with the explicit local Langlands correspondence for simple supercuspidal representations of general linear groups, this leads us to get an explicit description of the $L$-parameter as a representation of the Weil group of $F$. Our result is new when $p=2$ and our method provides a new proof even when $p\neq2$. |
| title | Simple supercuspidal L-packets of split special orthogonal groups over dyadic fields |
| topic | Number Theory Representation Theory 22E50, 11F70, 11L05 |
| url | https://arxiv.org/abs/2305.09076 |