Timeline for Global symplectic (orthogonal) type of automorphic representation compels its type to all its local components?
Current License: CC BY-SA 4.0
7 events
when toggle format | what | by | license | comment | |
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Jan 4, 2022 at 2:19 | vote | accept | Andrew | ||
Jan 2, 2022 at 14:13 | answer | added | David Loeffler | timeline score: 4 | |
Jan 2, 2022 at 13:15 | comment | added | Andrew | @DavidLoeffler, thank you very much for the helpful comment! The definition of orthogonal (or symplectic) of $\pi_v$ I mean is that if $\phi: WD_F \to \operatorname{GL}(n)$ is the Weil-Deligne representation corresponding to $\pi_v$, then we say $\pi_v$ is orthogonal (or symplectic) if the image of $\phi$ can be replaced to $\operatorname{SO}(n)$ (or $\operatorname{Sp}(n)$.) So if $\pi$ is symplectic (orthogonal), then it seems $\pi_v$’s are symplectic (or orthogonal) for all places $v$. | |
Jan 2, 2022 at 8:03 | comment | added | David Loeffler | It's easy to see that ($\pi$ is either symplectic or orthogonal) $\Leftrightarrow$ ($\pi$ is selfdual) $\Leftrightarrow$ ($\pi_v$ is selfdual for all $v$), but it's not so obvious if the local factors are symplectic / orthogonal if $\pi$ is. | |
Jan 1, 2022 at 20:12 | history | edited | LSpice | CC BY-SA 4.0 |
`\operatorname`, `\bigotimes`, and backwards apostrophe
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Jan 1, 2022 at 18:29 | history | edited | Andrew | CC BY-SA 4.0 |
edited title
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Jan 1, 2022 at 18:18 | history | asked | Andrew | CC BY-SA 4.0 |