Timeline for Good even grading and principal Levi type
Current License: CC BY-SA 3.0
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| Oct 12, 2012 at 20:58 | comment | added | Ben Webster♦ | The question was about even gradings, so thats fine. The issue I hadn't understood before was that you could take the grading for a parabolic, and not have a homogeneous Richardson element of degree 2. I hadn't processed that this was a serious condition. It's still very unclear to me how many Richardson elements don't have compatible even good gradings. | |
| Oct 12, 2012 at 20:52 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
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| Oct 11, 2012 at 13:30 | comment | added | Jim Humphreys |
Note that Thm. 2.1 presupposes an even grading. But a Richardson element might or might not have a good even grading and might or might not be of standard Levi type. (A subregular nilpotent in $G_2$ is Richardson but not standard Levi type, and its Dynkin grading is a good even grading as in 2.1.) The fourth paragraph of their $\S2$ discusses the minimal orbit, as in my added text here, where for $B_2$ the orbit is not Richardson but is standard Levi. Only type $A_n$ is well-behaved, with all orbits Richardson and standard Levi.
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| Oct 11, 2012 at 11:44 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |