Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908285192372224 |
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| author | Takanashi, Yugo |
| author_facet | Takanashi, Yugo |
| contents | We prove a general formula that relates the parity of the Langlands parameter of a conjugate self-dual discrete series representation of $\mathrm{GL}_n$ to the parity of its Jacquet-Langlands image. It gives a generalization of a partial result by Mieda concerning the case of invariant $1/n$ and supercuspidal representations. It also gives a variation of the result on the self-dual case by Prasad and Ramakrishnan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08830 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields Takanashi, Yugo Number Theory Representation Theory 11F70, 22E50, 22E55 We prove a general formula that relates the parity of the Langlands parameter of a conjugate self-dual discrete series representation of $\mathrm{GL}_n$ to the parity of its Jacquet-Langlands image. It gives a generalization of a partial result by Mieda concerning the case of invariant $1/n$ and supercuspidal representations. It also gives a variation of the result on the self-dual case by Prasad and Ramakrishnan. |
| title | Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields |
| topic | Number Theory Representation Theory 11F70, 22E50, 22E55 |
| url | https://arxiv.org/abs/2204.08830 |