Timeline for Generalizing a theorem of Kostant to arbitrary parabolics
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2017 at 14:23 | comment | added | Andy Sanders | Just for clarification, in my comment above, I should have said unique open $L$-orbit where $L$ is the appropriate Levi of the parabolic $P.$ Thank you for your suggestion Jim, I'll try to track this original reference down. | |
| Oct 28, 2017 at 20:05 | comment | added | Jim Humphreys | P.S. It does make sense to me to seek a generalization to all parabolics, though the formulation may involve some subtlety. What you've suggested in your short comment seems reasonable. | |
| Oct 28, 2017 at 20:00 | comment | added | Jim Humphreys | @Andy: It might help to add a specific reference to the earliest source where Kostant's theorem occurs. (Many though not all of his papers are by now freely accessible online.) In recent decades MathSciNet has included citation information, so it might be possible to track further developments (if any) in the parabolic case. | |
| Oct 27, 2017 at 18:10 | comment | added | Andy Sanders | Thank you for the reminder. I have in mind something specific for a generalization, but per mathoverflow standards I think I need to let this question stand as is. If it helps at all, I think $V$ in this generalization should be the $\mathfrak{p}$-translate of the unique open $P$-orbit in the $-1$ part of the grading corresponding to the parabolic $P.$ | |
| Oct 27, 2017 at 3:42 | comment | added | Victor Protsak | I am not sure what kind of generalization you are looking for, but the content of the theorem is that the adjoint $B$-action on $V$ admits a linear section $L$. If I remember correctly, this is termed "Kostant section" in the literature --- perhaps, that would be useful in searches. | |
| Oct 26, 2017 at 17:15 | history | asked | Andy Sanders | CC BY-SA 3.0 |