Timeline for Bruhat decomposition and standard Frobenius
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 7, 2022 at 16:17 | comment | added | LSpice | I think I may realise what I wasn't seeing. You are assuming that $B$ and $Q$, but not $G$, are defined over $\mathbb F_p$? (I'm not sure what you mean by asking about $\mathbb C$, since we're over $\overline{\mathbb F_p}$ here; maybe you mean to replace $(\overline{\mathbb F_p}, F_p)$ by $(\mathbb C, \text{conjugation})$?) | |
| Jun 7, 2022 at 16:12 | comment | added | fool rabbit | Thanks. But if it defined over $\mathbb{C}$, then how to define $W^Q$? | |
| Jun 7, 2022 at 13:09 | comment | added | LSpice | That link also unfortunately doesn't define it. A common definition is $W^Q = N_{G^{F_p}}(M)/M^{F_p}$ (and then the decomposition holds as desired), in which case the result is obvious; so, if you want to use some other definition, then you'll need to say what it is. | |
| Jun 7, 2022 at 4:18 | comment | added | fool rabbit | @LSpice :Dear LSpice, mathoverflow.net/q/195456/147080 I just use the notation of this question😂 | |
| Jun 6, 2022 at 20:52 | history | edited | LSpice | CC BY-SA 4.0 |
TeXing
|
| Jun 6, 2022 at 20:51 | comment | added | LSpice |
Do you mean by $W^Q$ the group $N_{G^{F_p}}(M)/M^{F_p}$, for $M$ a Levi component of $Q$? If so, then this is trivial, so you must not; but then I don't know what you do mean. (Also, please use "$F_p$-stable" $F_p$-stable, not "$F_p-$stable" $F_p-$stable. I have edited accordingly.)
|
|
| Jun 6, 2022 at 18:55 | history | asked | fool rabbit | CC BY-SA 4.0 |