Timeline for ideal generated by highest weight vectors
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 27, 2013 at 23:41 | comment | added | Jim Humphreys | Your question still seems hard to sort out, so anything you can add to illustrate or motivate it would be useful. For instance, what happens if your group just has rank 1? Aside from that, I'm guessing you want to work only in characteristic 0. Otherwise the representation theory gets far more complicated and involves serious unknowns. | |
| May 13, 2013 at 5:28 | comment | added | J. Knecht | Yes assume $I_0$ is homogeneous and that $G$ acts linearly. For me, $I$ is actually a polynomial representation of $G$. | |
| May 13, 2013 at 3:45 | comment | added | Allen Knutson | May I assume $I_0$ homogeneous, and $G$ acting linearly? I'm just trying to understand the geometry so far. ${\mathbb P}V(I_0)$ is a $B$-invariant projective variety, and you're looking at the intersection of all its $G$-translates. That closed subscheme will contain some closed $G$-orbits, and it's enough to know that it's reduced along those... I doubt this is helping. | |
| May 13, 2013 at 0:14 | history | asked | J. Knecht | CC BY-SA 3.0 |