Timeline for Do we have $K \cap P = (K \cap M)(K \cap N)$?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2019 at 10:15 | comment | added | Claudius | Maybe this article by G. Henniart and M.-F. Vigneras is helpful: A Satake isomorphism for representations modulo $p$ of reductive groups over local fields, especially 6.5 Theorem. | |
| Dec 13, 2018 at 19:28 | comment | added | LSpice | (By the way, my initial comment should have specified that it referred to positive-depth MP subgroups, which is why, as @PaulBroussous points out, it's insufficient.) | |
| Dec 13, 2018 at 19:27 | comment | added | LSpice | @PaulBroussous, I'm sure it follows from the material there (what doesn't?), but I don't find an exact statement. | |
| Dec 13, 2018 at 19:19 | comment | added | Paul Broussous | @LSpice In their article "Structure Theory Via Types", Bushnell and Kutzko claim that this is true if $K$ is special and refer to Tits, Corvalis. I do not have Tits's article with me. | |
| Dec 13, 2018 at 19:15 | comment | added | LSpice | @PaulBroussous, thanks; I missed that. | |
| Dec 13, 2018 at 19:09 | comment | added | Paul Broussous | @LSpice This is true but unfortunately insufficient since D_S wants K maximal. | |
| Dec 13, 2018 at 2:45 | comment | added | LSpice | This is a weakened form (i.e., it holds for more subgroups) of the notion of $K$ having an Iwahori decomposition with respect to $P$, which demands that $K = (\overline N \cap K)(M \cap K)(N \cap K)$ (from which your desired equality follows since $P \cap \overline N = \{1\}$). In particular, it holds for all Moy–Prasad filtration subgroups with respect to points $x$ in the building of $M$. | |
| Dec 12, 2018 at 21:11 | history | edited | D_S | CC BY-SA 4.0 |
added 467 characters in body
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| Dec 10, 2018 at 19:11 | history | asked | D_S | CC BY-SA 4.0 |