Timeline for The centralizer of a semisimple element which is not contained in any proper parabolic subgroups
Current License: CC BY-SA 4.0
6 events
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| Feb 6, 2019 at 15:37 | comment | added | LSpice | @D_S, if $A$ is a non-central split torus in $C_G(g)^\circ$, then $C_G(A)$ is the Levi component of a proper ($k$-)parabolic subgroup of $G$ containing $g$. | |
| Jan 9, 2019 at 17:08 | comment | added | D_S | But so far I don't see how we can get the converse implication. | |
| Jan 9, 2019 at 17:06 | comment | added | D_S | Thanks for your answer. Your last paragraph seems to show just one direction: $A_G$ is a maximal split torus of $C_G^{\circ}(g)$ $\Rightarrow$ $A_G$ is the split component of $C_G^{\circ}(g)$ $\Rightarrow$ $C_G(A_G) =G$ is the unique minimal Levi containing $C_G^{\circ}(g)$. It follows that $C_G^{\circ}(g)$, hence $g$, is not a member of any proper $k$-parabolic subgroup. | |
| S Jan 9, 2019 at 4:54 | history | suggested | D_S | CC BY-SA 4.0 |
Corollary 4.16 was slightly misstated
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| Jan 9, 2019 at 3:59 | review | Suggested edits | |||
| S Jan 9, 2019 at 4:54 | |||||
| Jan 8, 2019 at 14:11 | history | answered | Jay Taylor | CC BY-SA 4.0 |