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Mar 21, 2022 at 12:00 history edited Glorfindel CC BY-SA 4.0
broken link fixed
Oct 13, 2012 at 20:38 comment added Jim Humphreys P.S. I've restated my answer, to avoid the clutter in my old versions found in the edits.
Oct 13, 2012 at 20:37 history edited Jim Humphreys CC BY-SA 3.0
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Oct 11, 2012 at 11:23 history edited Jim Humphreys CC BY-SA 3.0
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Oct 11, 2012 at 11:18 history edited Jim Humphreys CC BY-SA 3.0
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Oct 10, 2012 at 17:13 history edited Jim Humphreys CC BY-SA 3.0
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Oct 10, 2012 at 16:34 comment added Jim Humphreys Yes, that gets more subtle. I know that each $e$ in the well-behaved type $A_n$ is of standard Levi type (but may not define an "even" orbit) and also has some good even grading. But my recollection is that in other types you sometimes have standard Levi type without any good even grading. I don't have Elashvili-Kac classification at hand right now to check examples.
Oct 10, 2012 at 14:06 comment added Alexander Braverman Thank you! I actually know most of the above, but what I wasn't able to figure out is this: how often does it happen that for $e$ which is regular in a Levi there is no good even grading?
Oct 10, 2012 at 12:40 history answered Jim Humphreys CC BY-SA 3.0