Timeline for Intersections of $B$ and $B^-$ orbits in the flag variety $G/B$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2015 at 18:18 | vote | accept | Qiao | ||
| Jan 14, 2015 at 18:15 | vote | accept | Qiao | ||
| Jan 14, 2015 at 18:18 | |||||
| Jan 14, 2015 at 17:20 | answer | added | Allen Knutson | timeline score: 6 | |
| Jan 14, 2015 at 14:44 | comment | added | Jim Humphreys | @Ben: Yes, that seems right in retrospect. I guess the important point is that the Bruhat ordering comes into play in nontrivial cases, which wasn't expressed in the question itself. | |
| Jan 14, 2015 at 14:24 | comment | added | Ben Webster♦ | @JimHumphreys The intersection is empty if the elements aren't comparable in Bruhat order. | |
| Jan 13, 2015 at 23:30 | comment | added | Jim Humphreys | @Piotr: Terminology varies, but in the paper you cite (later published in Crelle Journal) they seem to require that the two elements of $W$ involved are related by the Bruhat ordering. Arbitrary intersections must get more complicated to study. Probably the earliest paper in this direction is by Deodhar: ams.org/mathscinet-getitem?mr=782232 | |
| Jan 13, 2015 at 22:23 | comment | added | Piotr Achinger | It is also stated there that their closures are Cohen-Macaulay, so in particular they are equi-dimensional. | |
| Jan 13, 2015 at 22:20 | comment | added | Piotr Achinger | I think they are called (open) Richardson varieties. Their dimensions are described here: arxiv.org/pdf/1008.3939v2.pdf (page 2). | |
| Jan 13, 2015 at 22:15 | history | asked | Qiao | CC BY-SA 3.0 |