Timeline for Canonicality of group of integers for reductive groups over non-Archimedean local field
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2023 at 16:57 | comment | added | David Loeffler | A hyperspecial maximal compact subgroup is, in particular, a maximal compact subgroup. So I don't understand your question. | |
| Oct 1, 2023 at 11:44 | comment | added | user267839 | another point: do I understand it correctly that in case there exist such hyperspecial maximal compact $U$ (...and so $\mathcal{G}(\mathcal{O}_K)$ has isomorphic image to $U$ as the statement claims) that $U$ "plays" in non-Archimedean world the role of a maximal compact group $K$ wrt representation theory of $G$, even thought $U$ is not neccessary a maximal compact subgroup of $G$ as it would be the case for $K$ in classical Lie group setting, right? | |
| Sep 13, 2023 at 23:39 | comment | added | anon | Or better, the new book by Kaletha and Prasad: MR4520154 - Bruhat-Tits theory—a new approach Kaletha, Tasho; Prasad, Gopal New Math. Monogr., 44 Cambridge University Press, Cambridge, 2023, xxx+718 pp. | |
| Sep 10, 2023 at 12:05 | vote | accept | user267839 | ||
| Sep 10, 2023 at 10:42 | comment | added | LSpice | Splitting over an unramified extension shows the extensive of a hyperspecial. You can refer to the original Bruhat--Tits, or better to Tits's exposition, or even better to Rabinoff's or Yu's modern expositions. On my phone, so can't get links easily now. | |
| Sep 10, 2023 at 9:55 | comment | added | user267839 | * integral model | |
| Sep 10, 2023 at 9:33 | comment | added | user267839 | are there some let me call them "standard" assumptions on $G$, which garantee the existence of such "nice" open compact $U \subset G(K)$? eg "splittness" of $G$ as LSpice suggested? Do you know some classical reference where the construction of such integral is discussed? | |
| Sep 10, 2023 at 7:43 | history | answered | David Loeffler | CC BY-SA 4.0 |