Timeline for Fixed points of an involution
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2017 at 15:53 | comment | added | jack | Your arguments are fantastic. I have no problem with that. Of course my guess is wrong since the fixed locus is disconnected in this case. I thought the map is compatible with the standard symplectic form after some change of coordinates. | |
| Apr 4, 2017 at 15:25 | comment | added | Ben Webster♦ | @jack I understand why you might think that, but if it's the case, please explain the map and tell me the problem with my argument above. Checking any example would have shown you this guess is wrong. The fact that the map doesn't use a symplectic form should be a dead giveaway. If you want the symplectic Grassmannian, pick a symplectic form, and look at the involution given by taking symplectic orthogonal. | |
| Apr 4, 2017 at 14:12 | comment | added | jack | The above involution is induced by the Dynkin automorphism $\alpha_i \mapsto \alpha_{2n-i}$ and the parabolic $P_n$ is stable under this involution. So isn't the fixed locus same as one of the Symplectic Grassmannian ? | |
| Apr 4, 2017 at 13:34 | comment | added | Ben Webster♦ | @Mark The rest of the answer is an explanation of how to prove it. The map is given by looking at the intersection with the eigenspaces. | |
| Apr 4, 2017 at 0:43 | comment | added | Mark | Could you please give a reference of the 1st line of your answer or a hint to prove this ? Thanks. | |
| Apr 3, 2017 at 19:31 | vote | accept | Mark | ||
| Apr 3, 2017 at 18:25 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |