Timeline for Wang's C-subgroups and M-manifolds
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2015 at 12:50 | comment | added | Allen Knutson | $K = Spin(5), S = Spin(2), C_K(S) = Spin(2) \times Spin(3), C_K(S)' = 1 \times Spin(3) = U.$ This may be the point at which you should write the author. | |
| Feb 11, 2015 at 8:24 | comment | added | David P | Ok but Wang's setting is with $K$ simple. | |
| Feb 10, 2015 at 19:49 | comment | added | Allen Knutson | $K = SU(2)^2, S = T \times 1, C_K(S) = T \times SU(2), C_K(S)' = 1 \times SU(2) = U$. | |
| Feb 9, 2015 at 15:30 | comment | added | David P | I see your point. What if we add the assumption $U \neq 1$? | |
| Feb 9, 2015 at 14:46 | comment | added | Allen Knutson | Let's take $K=SU(2)$, $S$ a maximal torus, $C_K(S) = S$, $U = 1 = S'$. So $U$ is semisimple and a C-subgroup. But any centralizer $Q$ contains a maximal torus, so $U\neq Q$. | |
| Feb 8, 2015 at 8:37 | comment | added | David P | Ok, all tori are C-subgroups but there might be others and I'm asking about the semisimple ones. | |
| Feb 7, 2015 at 17:40 | comment | added | Allen Knutson | According to your second paragraph, $U$ is a C-subgroup if $U' = Z(S)'$ for $S$ a torus. If $S$ is a maximal torus, then $Z(S) = S$ so $Z(S)' = S' = 1$. Then if $U$ is any torus, $U' = 1$ too, making it a C-subgroup. | |
| Feb 7, 2015 at 16:56 | comment | added | David P | you mean every torus is a C-subgroup? | |
| Feb 7, 2015 at 3:55 | comment | added | Allen Knutson | The centralizer of a torus contains a maximal torus. But any torus in $G$ (assuming $G$ is semisimple) satisfies your stated criterion, even if it isn't maximal. So I suspect you've misread something. | |
| Feb 6, 2015 at 14:58 | history | asked | David P | CC BY-SA 3.0 |