Timeline for (Non-)Existence of certain invariant distributions on a p-adic space
Current License: CC BY-SA 3.0
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| Sep 5, 2017 at 13:23 | history | edited | Q-Zh | CC BY-SA 3.0 |
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| Aug 31, 2017 at 11:30 | history | edited | Q-Zh |
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| Aug 31, 2017 at 1:11 | history | edited | Q-Zh | CC BY-SA 3.0 |
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| Aug 30, 2017 at 17:38 | comment | added | reuns | I would use the word principal value (and show the similarity with $D'(\mathbb{R}^*) \ni 1/x \mapsto pv(1/x) \in D'(\mathbb{R})$) as it is really what you want to adapt to local fields | |
| Aug 30, 2017 at 15:14 | comment | added | Abdelmalek Abdesselam | @QingZhang: Yes and no. $G$-invariance is defined relatively to a multiplicative character so I guess we used different ones. It would help if you gave the definition of $G$-invariance in your question. | |
| Aug 30, 2017 at 14:28 | history | edited | Q-Zh | CC BY-SA 3.0 |
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| Aug 30, 2017 at 13:54 | history | edited | Q-Zh | CC BY-SA 3.0 |
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| Aug 30, 2017 at 13:50 | comment | added | Q-Zh | @AbdelmalekAbdesselam I think that one is not $G$-invariant. Because $d(ax)=|a|dx$ and the $G$-action is $(a,b).(x,y,z)=(ax,by,abz)$, we have $d(ax) d(by) d(abz)=|a|^2|b|^2 dxdydz.$ Am I right? | |
| Aug 30, 2017 at 13:39 | comment | added | Q-Zh | @AbdelmalekAbdesselam Do you mean $\varphi\mapsto 1$ for every $\varphi$? This one is not linear. But I probably misunderstood your point. | |
| Aug 30, 2017 at 13:35 | comment | added | Abdelmalek Abdesselam | @QingZhang: for question 1 what about the distribution given by the constant function equal to 1? | |
| Aug 30, 2017 at 13:29 | history | edited | Q-Zh | CC BY-SA 3.0 |
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| Aug 30, 2017 at 12:47 | history | edited | Q-Zh | CC BY-SA 3.0 |
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| Aug 30, 2017 at 12:39 | comment | added | Q-Zh | @GeraldEdgar Thanks for your comments. I will try to add these definitions to the question. | |
| Aug 30, 2017 at 12:38 | comment | added | Gerald Edgar | Thanks. The word "distribution" is used in other senses in mathematics as well, so this is useful. Maybe lack of definition was even the reason that other question got little attention. | |
| Aug 30, 2017 at 12:33 | comment | added | Q-Zh | @GeraldEdgar A distribution on an $\ell$-space (Hausdorff, locally compact, totally disconnected topological space) $X$ is just a linear dual of $S(X)$, where $S(X)$ is the space of compact supported locally constant functions on $X$, i.e., a distribution is an element in $Hom_{\textbf{C}}(S(X),\textbf{C})$. The standard reference is Bernstein-Zelevinski, "Representations of $GL(n,F)$, where $F$ is a non-Archimedean local field" | |
| Aug 30, 2017 at 12:10 | comment | added | Gerald Edgar | Reference for the notion "distribution" that you use? | |
| Aug 30, 2017 at 10:21 | history | asked | Q-Zh | CC BY-SA 3.0 |