Timeline for Non-vanishing of elements in cohomology of full Flag varieties
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2014 at 10:04 | vote | accept | aglearner | ||
| Jul 21, 2014 at 20:14 | answer | added | David E Speyer | timeline score: 5 | |
| Jul 21, 2014 at 15:46 | comment | added | aglearner | abx, yes thank you, I understand (I added one more tag - combinatorics). I ask this question here because for the moment I can not answer this combinatorial question. | |
| Jul 21, 2014 at 15:44 | history | edited | aglearner |
edited tags
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| Jul 21, 2014 at 15:34 | comment | added | abx | As hinted in the previous comments, this is a purely combinatorial problem. We have $H^*(F_n,\mathbb{Q})=\mathbb{Q}[t_1,\ldots ,t_n]/(s_1,\ldots ,s_n)$, where the $t_i$'s are the first Chern classes of the successive tautological quotient line bundles and $s_i$ is the $i$-th symmetric function. The question is to find the order of nilpotence of $t_1(t_1+t_2)\ldots (t_1+\ldots +t_{n-1})$ in that ring (and same question with the last factor deleted). | |
| Jul 21, 2014 at 15:15 | comment | added | aglearner | No Peter, I am interested in classes $\sigma_i$. If one replaces $\sigma_i$ by $\sigma_i-\sigma_{i-1}$ as you suggest, the question becomes completely different (and easy to answer) | |
| Jul 21, 2014 at 15:11 | comment | added | Peter Crooks | I think you should be taking the first Chern classes of the duals of quotients of adjacent bundles in your flag. | |
| Jul 21, 2014 at 14:45 | history | asked | aglearner | CC BY-SA 3.0 |