Variation of additive characters in the transfer for Mp(2n)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911400006254592 |
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| author | Li, Wen-Wei |
| author_facet | Li, Wen-Wei |
| contents | Let $\mathrm{Mp}(2n)$ be the metaplectic group of rank $n$ over a local field $F$ of characteristic zero. In this note, we determine the behavior of endoscopic transfer for $\mathrm{Mp}(2n)$ under variation of additive characters of $F$. The arguments are based on properties of transfer factor, requiring no deeper results from representation theory. Combined with the endoscopic character relations of Luo, this provides a simple and uniform proof of a theorem of Gan-Savin, which describes how the local Langlands correspondence for $\mathrm{Mp}(2n)$ depends on the additive characters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_03091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variation of additive characters in the transfer for Mp(2n) Li, Wen-Wei Representation Theory 22E50 (Primary) 11F70l, 11F72 (Secondary) Let $\mathrm{Mp}(2n)$ be the metaplectic group of rank $n$ over a local field $F$ of characteristic zero. In this note, we determine the behavior of endoscopic transfer for $\mathrm{Mp}(2n)$ under variation of additive characters of $F$. The arguments are based on properties of transfer factor, requiring no deeper results from representation theory. Combined with the endoscopic character relations of Luo, this provides a simple and uniform proof of a theorem of Gan-Savin, which describes how the local Langlands correspondence for $\mathrm{Mp}(2n)$ depends on the additive characters. |
| title | Variation of additive characters in the transfer for Mp(2n) |
| topic | Representation Theory 22E50 (Primary) 11F70l, 11F72 (Secondary) |
| url | https://arxiv.org/abs/2411.03091 |