Timeline for Orbit of a parahoric subgroup on a flag variety
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2023 at 8:08 | vote | accept | David Loeffler | ||
| Jul 13, 2023 at 3:46 | answer | added | jlansky | timeline score: 3 | |
| S Jun 23, 2023 at 20:03 | history | bounty ended | CommunityBot | ||
| S Jun 23, 2023 at 20:03 | history | notice removed | CommunityBot | ||
| Jun 19, 2023 at 9:53 | comment | added | David Loeffler | I wouldn't go that far, it's definitely helpful to have a reference, and the general setting of "double Tits systems" considered loc. cit. does sound as if it might be relevant for my general question. | |
| Jun 19, 2023 at 7:18 | comment | added | Paul Broussous | Sorry, you're right, it doesn't help at all. | |
| Jun 18, 2023 at 15:09 | comment | added | David Loeffler | @PaulBroussous As I wrote in the question, I know the result holds for any parahoric contained in G(O), and in particular for the Iwahori. So it is clear that the RHS surjects onto the LHS. What is not so clear to me is how to prove injectivity. | |
| Jun 17, 2023 at 14:35 | comment | added | Paul Broussous | I think that what you want should follows from the following decomposition of $G$. Let $I$ be a standard Iwahori subgroup and $B$ be a standard Borel subgroup. Then $G=I\cdot N(T)\cdot B$ (cf; Bruhat-Tits IHES - I, Thm (5.1.3)(iv), page 83. From this you get that the RHS of your conjectural identity contains a system of representatives. | |
| S Jun 15, 2023 at 18:07 | history | bounty started | David Loeffler | ||
| S Jun 15, 2023 at 18:07 | history | notice added | David Loeffler | Draw attention | |
| Jun 15, 2023 at 8:10 | history | edited | David Loeffler | CC BY-SA 4.0 |
T meant two things at once, sorry
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| Jun 13, 2023 at 11:15 | history | asked | David Loeffler | CC BY-SA 4.0 |